$$\frac{5}{2x}+\frac{3}{4} = \frac{1}{x}$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 1 }{ 2 } & x_2 = -\dfrac{ 4 }{ 5 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{5}{2x}+\frac{3}{4} &= \frac{1}{x}&& \text{multiply ALL terms by } \color{blue}{ 2x\cdot4 }. \\[1 em]2x\cdot4\cdot\frac{5}{2x}+2x\cdot4\cdot\frac{3}{4} &= 2x\cdot4\cdot\frac{1}{x}&& \text{cancel out the denominators} \\[1 em]20x^2+6x &= 8&& \text{move all terms to the left hand side } \\[1 em]20x^2+6x-8 &= 0&& \\[1 em] \end{aligned} $$
$ 20x^{2}+6x-8 = 0 $ is a quadratic equation.
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