$$\frac{9}{3}x = \frac{4}{x}+2$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 1 }{ 3 }-\dfrac{\sqrt{ 13 }}{ 3 } & x_2 = \dfrac{ 1 }{ 3 }+\dfrac{\sqrt{ 13 }}{ 3 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{9}{3}x &= \frac{4}{x}+2&& \text{multiply ALL terms by } \color{blue}{ 3x }. \\[1 em]3x \cdot \frac{9}{3}x &= 3x\cdot\frac{4}{x}+3x\cdot2&& \text{cancel out the denominators} \\[1 em]9x^2 &= 12+6x&& \text{move all terms to the left hand side } \\[1 em]9x^2-12-6x &= 0&& \text{simplify left side} \\[1 em]9x^2-6x-12 &= 0&& \\[1 em] \end{aligned} $$
$ 9x^{2}-6x-12 = 0 $ is a quadratic equation.
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