Question
$$1\cdot5x+\frac{64}{x} = 20$$
Answer
$$ \begin{matrix}x_1 = 2+\dfrac{ 2 \sqrt{ 55}}{ 5 }i & x_2 = 2-\dfrac{ 2 \sqrt{ 55}}{ 5 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 1\cdot5x+\frac{64}{x} &= 20&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x1\cdot5x+x\cdot\frac{64}{x} &= x\cdot20&& \text{cancel out the denominators} \\[1 em]5x^2+64 &= 20x&& \text{move all terms to the left hand side } \\[1 em]5x^2+64-20x &= 0&& \text{simplify left side} \\[1 em]5x^2-20x+64 &= 0&& \\[1 em] \end{aligned} $$
$ 5x^{2}-20x+64 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
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