ax^{2} + bx + c = 0

a (x^{2} + \frac{b}{a}x + \frac{c}{a}) = 0

(x + \frac{b}{2a})^{2} − \frac{b^{2}}{4a^{2}} + \frac{c}{a} = 0

(x + \frac{b}{2a})^{2} − \frac{b^{2} − 4ac}{4a^{2}} = 0

x + \frac{b}{2a} = \frac{±\sqrt{b^{2} − 4ac}}{2a}

x = \frac{−b ± \sqrt{b^{2} − 4ac}}{2a}