$$\frac{6}{x+4}+\frac{1}{x-4} = 5$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 7 }{ 10 }-\dfrac{\sqrt{ 1249 }}{ 10 } & x_2 = \dfrac{ 7 }{ 10 }+\dfrac{\sqrt{ 1249 }}{ 10 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{6}{x+4}+\frac{1}{x-4} &= 5&& \text{multiply ALL terms by } \color{blue}{ (x+4)(x-4) }. \\[1 em](x+4)(x-4)\cdot\frac{6}{x+4}+(x+4)(x-4)\cdot\frac{1}{x-4} &= (x+4)(x-4)\cdot5&& \text{cancel out the denominators} \\[1 em]6x-24+x+4 &= 5x^2-80&& \text{simplify left side} \\[1 em]7x-20 &= 5x^2-80&& \text{move all terms to the left hand side } \\[1 em]7x-20-5x^2+80 &= 0&& \text{simplify left side} \\[1 em]-5x^2+7x+60 &= 0&& \\[1 em] \end{aligned} $$
$ -5x^{2}+7x+60 = 0 $ is a quadratic equation.
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