Question
$$\frac{2}{x}+\frac{4}{3} = \frac{14}{3}x$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 1 }{ 7 }-\dfrac{\sqrt{ 22 }}{ 7 } & x_2 = \dfrac{ 1 }{ 7 }+\dfrac{\sqrt{ 22 }}{ 7 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{2}{x}+\frac{4}{3} &= \frac{14}{3}x&& \text{multiply ALL terms by } \color{blue}{ x\cdot3 }. \\[1 em]x\cdot3\cdot\frac{2}{x}+x\cdot3\cdot\frac{4}{3} &= x\cdot3 \cdot \frac{14}{3}x&& \text{cancel out the denominators} \\[1 em]6+4x &= 14x^2&& \text{move all terms to the left hand side } \\[1 em]6+4x-14x^2 &= 0&& \text{simplify left side} \\[1 em]-14x^2+4x+6 &= 0&& \\[1 em] \end{aligned} $$
$ -14x^{2}+4x+6 = 0 $ is a quadratic equation.
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