$$n-\frac{6}{n}-7 = \frac{9}{2}$$
Answer
$$ \begin{matrix}n_1 = -\dfrac{ 1 }{ 2 } & n_2 = 12 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} n-\frac{6}{n}-7 &= \frac{9}{2}&& \text{multiply ALL terms by } \color{blue}{ n\cdot2 }. \\[1 em]n\cdot2n-n\cdot2\cdot\frac{6}{n}-n\cdot2\cdot7 &= n\cdot2\cdot\frac{9}{2}&& \text{cancel out the denominators} \\[1 em]2n^2-12-14n &= 9n&& \text{simplify left side} \\[1 em]2n^2-14n-12 &= 9n&& \text{move all terms to the left hand side } \\[1 em]2n^2-14n-12-9n &= 0&& \text{simplify left side} \\[1 em]2n^2-23n-12 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}-23x-12 = 0 $ is a quadratic equation.
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