For all ax^2 + bx + c = 0

ax^2 + bx = -c

x^2 + (b/a)x = -c/a

Then, by completing the square of the binomial x^2 + (b/a)x,

x^2 + (b/a)x + (b^2)/(4a^2) = (b^2)/(4a^2) – (c/a)

(x + (b/2a))^2 = (b^2 – 4ac)/(4a^2)

abs (x + b/2a) = sqrt (b^2 – 4ac) / 2a

x = -b/2a +/- (sqrt (b^2 – 4ac) / 2a )

or, more traditionally,

x = (-b +/- sqrt ( b^2 – 4ac ) ) / 2a

in honor of John Z.