$$\frac{a}{4} = \frac{3}{a-4}$$
Answer
$$ \begin{matrix}a_1 = -2 & a_2 = 6 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{a}{4} &= \frac{3}{a-4}&& \text{multiply ALL terms by } \color{blue}{ 4(a-4) }. \\[1 em]4(a-4)\frac{a}{4} &= 4(a-4)\cdot\frac{3}{a-4}&& \text{cancel out the denominators} \\[1 em]a^2-4a &= 12&& \text{move all terms to the left hand side } \\[1 em]a^2-4a-12 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}-4x-12 = 0 $ is a quadratic equation.
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