# How do you solve  2x^2+7x+9=0?

Jun 3, 2015

$2 {x}^{2} + 7 x + 9$ is of the form $a {x}^{2} + b x + c$, with $a = 2$, $b = 7$ and $c = 9$.

The discriminant $\Delta$ is given by the formula:

$\Delta = {b}^{2} - 4 a c = {7}^{2} - \left(4 \times 2 \times 9\right) = 49 - 72 = - 23$

Since $\Delta < 0$ the quadratic equation has no real roots. It has two distinct complex roots.