$$\frac{1}{x}+\frac{3}{5x} = -5$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 25 }{ 6 }-\dfrac{\sqrt{ 565 }}{ 6 } & x_2 = -\dfrac{ 25 }{ 6 }+\dfrac{\sqrt{ 565 }}{ 6 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{x}+\frac{3}{5x} &= -5&& \text{multiply ALL terms by } \color{blue}{ x\cdot5 }. \\[1 em]x\cdot5\cdot\frac{1}{x}+x\cdot5\cdot\frac{3}{5x} &= x\cdot5\cdot(-5)&& \text{cancel out the denominators} \\[1 em]5+3x^2 &= -25x&& \text{simplify left side} \\[1 em]3x^2+5 &= -25x&& \text{move all terms to the left hand side } \\[1 em]3x^2+5+25x &= 0&& \text{simplify left side} \\[1 em]3x^2+25x+5 &= 0&& \\[1 em] \end{aligned} $$
$ 3x^{2}+25x+5 = 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