$$\frac{5}{x}+\frac{9}{8} = \frac{4}{8}x$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 9 }{ 8 }-\dfrac{\sqrt{ 721 }}{ 8 } & x_2 = \dfrac{ 9 }{ 8 }+\dfrac{\sqrt{ 721 }}{ 8 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{5}{x}+\frac{9}{8} &= \frac{4}{8}x&& \text{multiply ALL terms by } \color{blue}{ x\cdot8 }. \\[1 em]x\cdot8\cdot\frac{5}{x}+x\cdot8\cdot\frac{9}{8} &= x\cdot8 \cdot \frac{4}{8}x&& \text{cancel out the denominators} \\[1 em]40+9x &= 4x^2&& \text{move all terms to the left hand side } \\[1 em]40+9x-4x^2 &= 0&& \text{simplify left side} \\[1 em]-4x^2+9x+40 &= 0&& \\[1 em] \end{aligned} $$
$ -4x^{2}+9x+40 = 0 $ is a quadratic equation.
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