$$\frac{10}{2}x = \frac{1}{x}+4$$
Answer
$$ \begin{matrix}x_1 = 1 & x_2 = -\dfrac{ 1 }{ 5 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{10}{2}x &= \frac{1}{x}+4&& \text{multiply ALL terms by } \color{blue}{ 2x }. \\[1 em]2x \cdot \frac{10}{2}x &= 2x\cdot\frac{1}{x}+2x\cdot4&& \text{cancel out the denominators} \\[1 em]10x^2 &= 2+8x&& \text{move all terms to the left hand side } \\[1 em]10x^2-2-8x &= 0&& \text{simplify left side} \\[1 em]10x^2-8x-2 &= 0&& \\[1 em] \end{aligned} $$
$ 10x^{2}-8x-2 = 0 $ is a quadratic equation.
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