$$\frac{8}{y}+\frac{4}{5} = \frac{8}{5}y$$
Answer
$$ \begin{matrix}y_1 = -2 & y_2 = \dfrac{ 5 }{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{8}{y}+\frac{4}{5} &= \frac{8}{5}y&& \text{multiply ALL terms by } \color{blue}{ y\cdot5 }. \\[1 em]y\cdot5\cdot\frac{8}{y}+y\cdot5\cdot\frac{4}{5} &= y\cdot5 \cdot \frac{8}{5}y&& \text{cancel out the denominators} \\[1 em]40+4y &= 8y^2&& \text{move all terms to the left hand side } \\[1 em]40+4y-8y^2 &= 0&& \text{simplify left side} \\[1 em]-8y^2+4y+40 &= 0&& \\[1 em] \end{aligned} $$
$ -8x^{2}+4x+40 = 0 $ is a quadratic equation.
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