Question
$$\frac{9}{4}x-\frac{5}{x}+\frac{4}{3} = 0$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 8 }{ 27 }-\dfrac{ 2 \sqrt{ 421}}{ 27 } & x_2 = -\dfrac{ 8 }{ 27 }+\dfrac{ 2 \sqrt{ 421}}{ 27 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{9}{4}x-\frac{5}{x}+\frac{4}{3} &= 0&& \text{multiply ALL terms by } \color{blue}{ 4x\cdot3 }. \\[1 em]4x\cdot3 \cdot \frac{9}{4}x-4x\cdot3\cdot\frac{5}{x}+4x\cdot3\cdot\frac{4}{3} &= 4x\cdot3\cdot0&& \text{cancel out the denominators} \\[1 em]27x^2-60+16x &= 0&& \text{simplify left side} \\[1 em]27x^2+16x-60 &= 0&& \\[1 em] \end{aligned} $$
$ 27x^{2}+16x-60 = 0 $ is a quadratic equation.
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