I have been told that you guys can solve about any math problem!

I think I have answered my own question on solving Fourth Degree Equations, but in the process, I need to find the Arc Cosine of a number. What is an ArcCosine and how do I find it? I am writing a program in VB .Net. (I don't have a good enough mind to figure it out on my own!)

Originally, I had these Equations:
VB .Net Code:
  1. Me.lblFirst.Text = -b / (4 * a) _

  2.  - 1 / 2 * Math.Sqrt(b ^ 2 / (4 * a ^ 2) - 2 * c / _

  3.         (3 * a) + 2 ^ (1 / 3) * (c ^ 2 - 3 * b * d + 12 * a * f) / (3 * a * (2 * c ^ 3 - 9 * _

  4.         b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + Math.Sqrt(-4 * (c ^ _

  5.         2 - 3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 _

  6.         * b ^ 2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3)) + 1 / (3 * 2 ^ (1 / 3) * a) * (2 * c ^ _

  7.         3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + Math.Sqrt(-4 * _

  8.         (c ^ 2 - 3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + _

  9.         27 * b ^ 2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3)) _

  10.  - 1 / 2 * Math.Sqrt(b ^ 2 / (2 * _

  11.         a ^ 2) - 4 * c / (3 * a) - 2 ^ (1 / 3) * (c ^ 2 - 3 * b * d + 12 * a * f) / (3 * a * _

  12.         (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + _

  13.         Math.Sqrt(-4 * (c ^ 2 - 3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + _

  14.         27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3)) - 1 / (3 * 2 ^ (1 / _

  15.         3) * a) * (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * _

  16.         f + Math.Sqrt(-4 * (c ^ 2 - 3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * _

  17.         d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3) _

  18.  - (-b ^ 3 / a ^ _

  19.         3 + 4 * b * c / a ^ 2 - 8 * d / a) / (4 * Math.Sqrt(b ^ 2 / (4 * a ^ 2) - 2 * c / (3 * _

  20.         a) + 2 ^ (1 / 3) * (c ^ 2 - 3 * b * d + 12 * a * f) / (3 * a * ((2 * c ^ 3 - 9 * b * _

  21.         c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + Math.Sqrt(-4 * (c ^ 2 - 3 * _

  22.         b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * _

  23.         f - 72 * a * c * f) ^ 2))) ^ (1 / 3)) + 1 / (3 * 2 ^ (1 / 3) * a) * (2 * c ^ 3 - 9 * _

  24.         b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + Math.Sqrt(-4 * (c ^ 2 - _

  25.         3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ _

  26.         2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3))))

  27.  
  28.         Me.lblSecond.Text = -b / (4 * a) _

  29.  - 1 / 2 * Math.Sqrt(b ^ 2 / (4 * a ^ 2) - 2 * c / _

  30.         (3 * a) + 2 ^ (1 / 3) * (c ^ 2 - 3 * b * d + 12 * a * f) / (3 * a * (2 * c ^ 3 - 9 * _

  31.         b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + Math.Sqrt(-4 * (c ^ _

  32.         2 - 3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 _

  33.         * b ^ 2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3)) + 1 / (3 * 2 ^ (1 / 3) * a) * (2 * c ^ _

  34.         3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + Math.Sqrt(-4 * _

  35.         (c ^ 2 - 3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + _

  36.         27 * b ^ 2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3)) _

  37.  + 1 / 2 * Math.Sqrt(b ^ 2 / (2 * _

  38.         a ^ 2) - 4 * c / (3 * a) - 2 ^ (1 / 3) * (c ^ 2 - 3 * b * d + 12 * a * f) / (3 * a * _

  39.         (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + _

  40.         Math.Sqrt(-4 * (c ^ 2 - 3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + _

  41.         27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3)) - 1 / (3 * 2 ^ (1 / _

  42.         3) * a) * (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * _

  43.         f + Math.Sqrt(-4 * (c ^ 2 - 3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * _

  44.         d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3) _

  45.  - (-b ^ 3 / a ^ _

  46.         3 + 4 * b * c / a ^ 2 - 8 * d / a) / (4 * Math.Sqrt(b ^ 2 / (4 * a ^ 2) - 2 * c / (3 * _

  47.         a) + 2 ^ (1 / 3) * (c ^ 2 - 3 * b * d + 12 * a * f) / (3 * a * ((2 * c ^ 3 - 9 * b * _

  48.         c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + Math.Sqrt(-4 * (c ^ 2 - 3 * _

  49.         b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * _

  50.         f - 72 * a * c * f) ^ 2))) ^ (1 / 3)) + 1 / (3 * 2 ^ (1 / 3) * a) * (2 * c ^ 3 - 9 * _

  51.         b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + Math.Sqrt(-4 * (c ^ 2 - _

  52.         3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ _

  53.         2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3))))

  54.  
  55.         Me.lblThird.Text = -b / (4 * a) _

  56.  + 1 / 2 * Math.Sqrt(b ^ 2 / (4 * a ^ 2) - 2 * c / _

  57.         (3 * a) + 2 ^ (1 / 3) * (c ^ 2 - 3 * b * d + 12 * a * f) / (3 * a * (2 * c ^ 3 - 9 * _

  58.         b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + Math.Sqrt(-4 * (c ^ _

  59.         2 - 3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 _

  60.         * b ^ 2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3)) + 1 / (3 * 2 ^ (1 / 3) * a) * (2 * c ^ _

  61.         3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + Math.Sqrt(-4 * _

  62.         (c ^ 2 - 3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + _

  63.         27 * b ^ 2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3)) _

  64.  - 1 / 2 * Math.Sqrt(b ^ 2 / (2 * _

  65.         a ^ 2) - 4 * c / (3 * a) - 2 ^ (1 / 3) * (c ^ 2 - 3 * b * d + 12 * a * f) / (3 * a * _

  66.         (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + _

  67.         Math.Sqrt(-4 * (c ^ 2 - 3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + _

  68.         27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3)) - 1 / (3 * 2 ^ (1 / _

  69.         3) * a) * (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * _

  70.         f + Math.Sqrt(-4 * (c ^ 2 - 3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * _

  71.         d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3) _

  72.  + (-b ^ 3 / a ^ _

  73.         3 + 4 * b * c / a ^ 2 - 8 * d / a) / (4 * Math.Sqrt(b ^ 2 / (4 * a ^ 2) - 2 * c / (3 * _

  74.         a) + 2 ^ (1 / 3) * (c ^ 2 - 3 * b * d + 12 * a * f) / (3 * a * ((2 * c ^ 3 - 9 * b * _

  75.         c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + Math.Sqrt(-4 * (c ^ 2 - 3 * _

  76.         b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * _

  77.         f - 72 * a * c * f) ^ 2))) ^ (1 / 3)) + 1 / (3 * 2 ^ (1 / 3) * a) * (2 * c ^ 3 - 9 * _

  78.         b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + Math.Sqrt(-4 * (c ^ 2 - _

  79.         3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ _

  80.         2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3))))

  81.  
  82.         Me.lblFourth.Text = -b / (4 * a) _

  83.  + 1 / 2 * Math.Sqrt(b ^ 2 / (4 * a ^ 2) - 2 * c / _

  84.         (3 * a) + 2 ^ (1 / 3) * (c ^ 2 - 3 * b * d + 12 * a * f) / (3 * a * (2 * c ^ 3 - 9 * _

  85.         b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + Math.Sqrt(-4 * (c ^ _

  86.         2 - 3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 _

  87.         * b ^ 2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3)) + 1 / (3 * 2 ^ (1 / 3) * a) * (2 * c ^ _

  88.         3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + Math.Sqrt(-4 * _

  89.         (c ^ 2 - 3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + _

  90.         27 * b ^ 2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3)) _

  91.  + 1 / 2 * Math.Sqrt(b ^ 2 / (2 * _

  92.         a ^ 2) - 4 * c / (3 * a) - 2 ^ (1 / 3) * (c ^ 2 - 3 * b * d + 12 * a * f) / (3 * a * _

  93.         (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + _

  94.         Math.Sqrt(-4 * (c ^ 2 - 3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + _

  95.         27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3)) - 1 / (3 * 2 ^ (1 / _

  96.         3) * a) * (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * _

  97.         f + Math.Sqrt(-4 * (c ^ 2 - 3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * _

  98.         d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3) _

  99.  + (-b ^ 3 / a ^ _

  100.         3 + 4 * b * c / a ^ 2 - 8 * d / a) / (4 * Math.Sqrt(b ^ 2 / (4 * a ^ 2) - 2 * c / (3 * _

  101.         a) + 2 ^ (1 / 3) * (c ^ 2 - 3 * b * d + 12 * a * f) / (3 * a * ((2 * c ^ 3 - 9 * b * _

  102.         c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + Math.Sqrt(-4 * (c ^ 2 - 3 * _

  103.         b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * _

  104.         f - 72 * a * c * f) ^ 2))) ^ (1 / 3)) + 1 / (3 * 2 ^ (1 / 3) * a) * (2 * c ^ 3 - 9 * _

  105.         b * c * d + 27 * a * d ^ 2 + 27 * b ^ 2 * f - 72 * a * c * f + Math.Sqrt(-4 * (c ^ 2 - _

  106.         3 * b * d + 12 * a * f) ^ 3 + (2 * c ^ 3 - 9 * b * c * d + 27 * a * d ^ 2 + 27 * b ^ _

  107.         2 * f - 72 * a * c * f) ^ 2)) ^ (1 / 3))))

This was a little to complicated for me. It also was returning "N/A" (meaning: "Not a Number"). Any suggestions?

Since then I have been using this method because the aforesaid was not working. Thus, my problem of finding the ArcCosine.

I don't really care HOW I find the roots of the equation. I just want to be able to do it.

Just to let you know, if you give me the method, I can put it into VB .Net. Don't feel obligated to program for me. It somebody does know VB, that would be great!

Wow. That's a long post! I thank you for reading this far!