Divide by aaa: x2+(b/a)x+c/a=0x^2 + (b/a)x + c/a = 0x2+(b/a)x+c/a=0. Add and subtract (b/2a)2(b/2a)^2(b/2a)2: (x+b2a)2=b2−4ac4a2\left(x + \dfrac{b}{2a}\right)^2 = \dfrac{b^2 - 4ac}{4a^2}(x+2ab)2=4a2b2−4ac. Taking square roots gives the quadratic formula.