The quadratic formula is used to find the roots (solutions) of a quadratic equation of the form: $ ax^2+bx+c=0$ **Standard formula:** The general solution for the quadratic equation is given by $ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} $ where $b^2-4ac$ is the discriminant: - If $b^2 -4ac >0$, there are two distinct solutions. - If $b^2 -4ac =0$, there is one unique solution. - If $b^2 -4ac <0$, the roots are complex (no real solution). **Simplified formula:** In the special case where $a=0$ the quadratic equation has the form: $ x^2 +px -q =0$ This simplifies the solving formula to: $ x=-\frac{p}{2} \pm \sqrt{\frac{p^2}{4}-q} $