Transforming Formulae

[hypnos]

Hi All.
I've been reading in a book about how to transform formulae but can't really make any sense of it. It just shows examples and doesn't really explain. I've been searching the web too for information on this but not really having any luck. Here's one example from the book:

Transform the forumla

          8d^2
L = l + ------
             3l

into one which expresses d in terms of the other quantities.

It shows how it's done but doesn't supply any rules which I can follow when transforming a formula.

If anybody has information about this or can just direct me to a web site with a decent explanation I'd be very grateful.

Thanks a lot.

[bugzpodder]

use ur algebra skills, so:

          8d^2
L = l + ------
             3l

L-l=(8d^2)/(3l)
3l(L-l)=8d^2
d^2=(3l(L-l))/8 SRBS

abs(d)=sqrt((3l(L-l))/8)
d=+/- sqrt((3l(L-l))/2)/2

[snakeeyes1000]

start undoing things with the least precedence first. So we can first move the l to the left side:

        8d^2
L - l = ----
         3l

Then let's multiply both sides by 3l.

  
3l(L - l) = 8d^2

The next step would be to divide both sides by 8.

3l(L - l) 
--------- = d^2
     8

Next, we should expand the 3l(L-l)(distributive property)

3Ll-3l^2
--------- = d^2
     8

Finally, Get the Square-Root.

     3Ll-3l^2
SQRT(---------)= d
          8

Then, Simplify the 8 because it has a factor(4) that is a perfect square.

     3Ll-3l^2
SQRT(---------)/2= d
          2

The key is too simplify in opposite order of order of operations. This ensures that everything goes well.

[hypnos]

I understand what's going on here. I thank you for this. I guess I'll just work through a load of them until I become proficient with this operation.

Thanks again.