$$\frac{y}{3} = \frac{y+8}{y+5}$$
Answer
$$ \begin{matrix}y_1 = 4 & y_2 = -6 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{y}{3} &= \frac{y+8}{y+5}&& \text{multiply ALL terms by } \color{blue}{ 3(y+5) }. \\[1 em]3(y+5)\frac{y}{3} &= 3(y+5)\frac{y+8}{y+5}&& \text{cancel out the denominators} \\[1 em]y^2+5y &= 3y+24&& \text{move all terms to the left hand side } \\[1 em]y^2+5y-3y-24 &= 0&& \text{simplify left side} \\[1 em]y^2+2y-24 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}+2x-24 = 0 $ is a quadratic equation.
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