Answer
$$q=\frac{-2+\sqrt{30}}{2},\:q=\frac{-2-\sqrt{30}}{2}$$
Work Step by Step
Using the quadratic formula, we find:
$$ q=\frac{-4\pm \sqrt{4^2-4\cdot \:2\left(-13\right)}}{2\cdot \:2} \\ q=\frac{-2+\sqrt{30}}{2},\:q=\frac{-2-\sqrt{30}}{2}$$