From the quadratic formula:

(\x_1 = \frac{-b + \sqrt{b^2-4ac}}{2a}\)

(\x_2 = \frac{-b - \sqrt{b^2-4ac}}{2a}\)

Add the roots

\(x_1 +x_2 = \frac{-b + \sqrt{b^2-4ac}}{2a} + \frac{-b - \sqrt{b^2-4ac}}{2a}\)

\(x_1 +x_2 = \frac{-2b}{2a}\)

\(x_1 + x_2 = \frac{-b}{a}\): The sum of roots of a quadratic function