$$y-\frac{6}{y} = 5$$
Answer
$$ \begin{matrix}y_1 = -1 & y_2 = 6 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} y-\frac{6}{y} &= 5&& \text{multiply ALL terms by } \color{blue}{ y }. \\[1 em]yy-y\cdot\frac{6}{y} &= y\cdot5&& \text{cancel out the denominators} \\[1 em]y^2-6 &= 5y&& \text{move all terms to the left hand side } \\[1 em]y^2-6-5y &= 0&& \text{simplify left side} \\[1 em]y^2-5y-6 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}-5x-6 = 0 $ is a quadratic equation.
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