Answer
$$q=\frac{\sqrt{41}+1}{5},\:q=\frac{-\sqrt{41}+1}{5}$$
Work Step by Step
Completing the square, we find:
$$5\left(q^2-\frac{2q}{5}-\frac{8}{5}\right) \\ 5\left(q-\frac{1}{5}\right)^2-\frac{41}{5}$$
Setting this equal to zero:
$$5\left(q-\frac{1}{5}\right)^2=\frac{41}{5} \\ q=\frac{\sqrt{41}+1}{5},\:q=\frac{-\sqrt{41}+1}{5}$$
