Question
$$x+\frac{4}{x}-\frac{3}{5} = \frac{2}{x}$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 3 }{ 10 }+\dfrac{\sqrt{ 191 }}{ 10 }i & x_2 = \dfrac{ 3 }{ 10 }-\dfrac{\sqrt{ 191 }}{ 10 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x+\frac{4}{x}-\frac{3}{5} &= \frac{2}{x}&& \text{multiply ALL terms by } \color{blue}{ x\cdot5 }. \\[1 em]x\cdot5x+x\cdot5\cdot\frac{4}{x}-x\cdot5\cdot\frac{3}{5} &= x\cdot5\cdot\frac{2}{x}&& \text{cancel out the denominators} \\[1 em]5x^2+20-3x &= 10&& \text{simplify left side} \\[1 em]5x^2-3x+20 &= 10&& \text{move all terms to the left hand side } \\[1 em]5x^2-3x+20-10 &= 0&& \text{simplify left side} \\[1 em]5x^2-3x+10 &= 0&& \\[1 em] \end{aligned} $$
$ 5x^{2}-3x+10 = 0 $ is a quadratic equation.
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