Solution to Quadratic Equation

A quadratic equation is an algebraic equation of the form $$ax^2 + bx + c = 0$$.

Its solution is $$x = \frac {-b \pm \sqrt {b^2 - 4 a c}} {2a}$$.

Proof
Let $$ax^2 + bx + c = 0$$.

Then $$x^2 + \frac {bx} {a} + \frac {c}{a} = 0$$.

By completing the square:

$$\left ({x + \frac {b}{2a}}\right)^2 - \frac {b^2} {4a^2} + \frac {c}{a} = 0$$

$$\left ({x + \frac {b}{2a}}\right)^2 = \frac {b^2 - 4 a c} {4a^2}$$

$$x + \frac {b}{2a} = \pm \frac {\sqrt {b^2 - 4 a c}} {2a}$$

from whence the result:

$$x = \frac {-b \pm \sqrt {b^2 - 4 a c}} {2a}$$