$$\frac{7}{3}x-\frac{4}{x} = 1$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 3 }{ 14 }-\dfrac{\sqrt{ 345 }}{ 14 } & x_2 = \dfrac{ 3 }{ 14 }+\dfrac{\sqrt{ 345 }}{ 14 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{7}{3}x-\frac{4}{x} &= 1&& \text{multiply ALL terms by } \color{blue}{ 3x }. \\[1 em]3x \cdot \frac{7}{3}x-3x\cdot\frac{4}{x} &= 3x\cdot1&& \text{cancel out the denominators} \\[1 em]7x^2-12 &= 3x&& \text{move all terms to the left hand side } \\[1 em]7x^2-12-3x &= 0&& \text{simplify left side} \\[1 em]7x^2-3x-12 &= 0&& \\[1 em] \end{aligned} $$
$ 7x^{2}-3x-12 = 0 $ is a quadratic equation.
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