$$\frac{-a}{8a+40} = \frac{1}{a+6}$$
Answer
$$ \begin{matrix}a_1 = -4 & a_2 = -10 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{-a}{8a+40} &= \frac{1}{a+6}&& \text{multiply ALL terms by } \color{blue}{ (8a+40)(a+6) }. \\[1 em](8a+40)(a+6)\frac{-a}{8a+40} &= (8a+40)(a+6)\cdot\frac{1}{a+6}&& \text{cancel out the denominators} \\[1 em]-a^2-6a &= 8a+40&& \text{move all terms to the left hand side } \\[1 em]-a^2-6a-8a-40 &= 0&& \text{simplify left side} \\[1 em]-a^2-14a-40 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}-14x-40 = 0 $ is a quadratic equation.
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