Question
$$\frac{1}{2}q^2 = 4q-200$$
Answer
$$ \begin{matrix}q_1 = 4+8 \sqrt{ 6 }i & q_2 = 4-8 \sqrt{ 6 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{2}q^2 &= 4q-200&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{1}{2}q^2 &= 2\cdot4q-2\cdot200&& \text{cancel out the denominators} \\[1 em]q^2 &= 8q-400&& \text{move all terms to the left hand side } \\[1 em]q^2-8q+400 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}-8x+400 = 0 $ is a quadratic equation.
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