$$\frac{3}{x}+2-\frac{1}{5}x = \frac{1}{x}$$
Answer
$$ \begin{matrix}x_1 = 5-\sqrt{ 35 } & x_2 = 5+\sqrt{ 35 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{3}{x}+2-\frac{1}{5}x &= \frac{1}{x}&& \text{multiply ALL terms by } \color{blue}{ x\cdot5 }. \\[1 em]x\cdot5\cdot\frac{3}{x}+x\cdot5\cdot2-x\cdot5\frac{1}{5}x &= x\cdot5\cdot\frac{1}{x}&& \text{cancel out the denominators} \\[1 em]15+10x-x^2 &= 5&& \text{simplify left side} \\[1 em]-x^2+10x+15 &= 5&& \text{move all terms to the left hand side } \\[1 em]-x^2+10x+15-5 &= 0&& \text{simplify left side} \\[1 em]-x^2+10x+10 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+10x+10 = 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.
This page was created using
Equations Solver