Origin of the quadratic equation

If you have a function in the form of

ax^2+bx+c=0, we know that the if we want to solve for x, we use the quadratic equation:

(-b(+/-)Sqrt(b^2 - 4ac))/2a

How was this discovered?

Wiki Article

ax² + bx + c = 0

a[x² + (b/a)x] + c = 0

a[(x + (b/2a))² - (b²/4a²)] + c = 0

a(x + (b/2a))² - (b²/4a) + c = 0

a(x + (b/2a))² = (b²/4a) - c

(x + (b/2a))² = (b²/4a²) - (c/a)

(x + (b/2a))² = (b²/4a²) - (4ac/4a²)

(x + (b/2a))² = (b² - 4ac)/(4a²)

(x + (b/2a)) = +/- [\sqrt(b² - 4ac)]/(2a)

x = (-b/2a) +/- [\sqrt(b² - 4ac)]/(2a)

x = [-b +/- \sqrt(b² - 4ac)]/(2a)