Question
$$\frac{1}{4}+\frac{1}{5}x = \frac{2}{x}$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 5 }{ 8 }-\dfrac{\sqrt{ 665 }}{ 8 } & x_2 = -\dfrac{ 5 }{ 8 }+\dfrac{\sqrt{ 665 }}{ 8 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{4}+\frac{1}{5}x &= \frac{2}{x}&& \text{multiply ALL terms by } \color{blue}{ 4\cdot5x }. \\[1 em]4\cdot5x\cdot\frac{1}{4}+4\cdot5x\frac{1}{5}x &= 4\cdot5x\cdot\frac{2}{x}&& \text{cancel out the denominators} \\[1 em]5x+4x^2 &= 40&& \text{simplify left side} \\[1 em]4x^2+5x &= 40&& \text{move all terms to the left hand side } \\[1 em]4x^2+5x-40 &= 0&& \\[1 em] \end{aligned} $$
$ 4x^{2}+5x-40 = 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