Answer
$$q=\frac{-3+\sqrt{15}}{2},\:q=-\frac{3+\sqrt{15}}{2}$$
Work Step by Step
The quadratic formula states:
$$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$
Thus, solving the equation, we find:
$$ q_{1,\:2}=\frac{-6\pm \sqrt{6^2-4\cdot \:2\left(-3\right)}}{2\cdot \:2} \\ q=\frac{-3+\sqrt{15}}{2},\:q=-\frac{3+\sqrt{15}}{2}$$