$$(4q+1)(4q-2) = 0$$
Answer
$$ \begin{matrix}q_1 = \dfrac{ 1 }{ 2 } & q_2 = -\dfrac{ 1 }{ 4 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (4q+1)(4q-2) &= 0&& \text{simplify left side} \\[1 em]16q^2-8q+4q-2 &= 0&& \\[1 em]16q^2-4q-2 &= 0&& \\[1 em] \end{aligned} $$
$ 16x^{2}-4x-2 = 0 $ is a quadratic equation.
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