a x² + b x + c = 0
a (x² + b/a x + c/a) = 0
a (x² + b/a x + b²/ 4a² - b²/ 4a² + c/a) = 0
x² + b/a x + b²/ 4a² - b²/ 4a² + c/a = 0
x² + b/a x + b²/ 4a² = b²/ 4a² - c/a
(x + b/2a)² = (b² - 4a c)/ 4a²
x + b/2a = sqrt [(b² - 4a c)/ 4a²]
x = -b/2a +- sqrt (b² - 4a c)/ 2a
x = [-b +- sqrt (b² - 4a c)] / 2a
