$$\frac{7}{x}-\frac{3}{20} = \frac{1}{5x}$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 3 }{ 8 }-\dfrac{\sqrt{ 2249 }}{ 8 } & x_2 = -\dfrac{ 3 }{ 8 }+\dfrac{\sqrt{ 2249 }}{ 8 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{7}{x}-\frac{3}{20} &= \frac{1}{5x}&& \text{multiply ALL terms by } \color{blue}{ x\cdot20\cdot5 }. \\[1 em]x\cdot20\cdot5\cdot\frac{7}{x}-x\cdot20\cdot5\cdot\frac{3}{20} &= x\cdot20\cdot5\cdot\frac{1}{5x}&& \text{cancel out the denominators} \\[1 em]700-15x &= 20x^2&& \text{move all terms to the left hand side } \\[1 em]700-15x-20x^2 &= 0&& \text{simplify left side} \\[1 em]-20x^2-15x+700 &= 0&& \\[1 em] \end{aligned} $$
$ -20x^{2}-15x+700 = 0 $ is a quadratic equation.
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