Proof (
completing the square method):
ax2 +bx + c = 0
ax2 + bx = -c
x2 + bx / a = -c/a
x2 + bx / a + (b / 2a)2 = -c / a + (b / 2a)2
(x + (b / 2a))2 = -4ac / 4a2 + b2 / 4a2
x + (b / 2a)2 = (b2 - 4ac) / 4a2
x + (b / 2a) = +/- sqrt ((b2 - 4ac) / 4a2)
x = -b / 2a +/- sqrt(b2 - 4ac) / 2a
x = -b +/- sqrt(b2 - 4ac) / 2a