How to derive the equation for x in a quadratic equation? 
Possible Duplicate:
Why can ALL quadratic equations be solved by the quadratic formula? 

How to derive this:
$x = \frac{-b + {\sqrt{b^2 + 4ac}}}{2a}$
From this:
$ax^2 + bx + c = 0$
I know this may be a little elementary :)

from $ax^2 + bx + c = 0 \Leftrightarrow  4a^2x^2 + 4abx + b^2 = b^2 - 4ac$.
Hence $(2ax + b)^2 = b^2 - 4ac$ then $2ax + b = \pm \sqrt{b^2 - 4ac}$.
from this, we have $ x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
