$$\frac{3}{x} = \frac{4}{3}x-\frac{10}{3}$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 5 }{ 4 }-\dfrac{\sqrt{ 61 }}{ 4 } & x_2 = \dfrac{ 5 }{ 4 }+\dfrac{\sqrt{ 61 }}{ 4 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{3}{x} &= \frac{4}{3}x-\frac{10}{3}&& \text{multiply ALL terms by } \color{blue}{ x\cdot3 }. \\[1 em]x\cdot3\cdot\frac{3}{x} &= x\cdot3 \cdot \frac{4}{3}x-x\cdot3\cdot\frac{10}{3}&& \text{cancel out the denominators} \\[1 em]9 &= 4x^2-10x&& \text{move all terms to the left hand side } \\[1 em]9-4x^2+10x &= 0&& \text{simplify left side} \\[1 em]-4x^2+10x+9 &= 0&& \\[1 em] \end{aligned} $$
$ -4x^{2}+10x+9 = 0 $ is a quadratic equation.
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