The solutions of the equation $ax^2 + bx + c = 0$ are given by the quadratic formula: $x = \frac{-b \pm \sqrt\Delta}{2a}$ where $\Delta$ is the ‘discriminant’: $\Delta = b^2 - 4ac.$ If $\Delta \gt 0$, there are two solutions; if $\Delta = 0$, there is one solution; if $\Delta \lt 0$, there are no real solutions.