Question
$$-\frac{3}{x} = \frac{5}{2}x$$
Answer
$$ \begin{matrix}x_1 = \dfrac{\sqrt{ 30 }}{ 5 } i & x_2 = - \dfrac{\sqrt{ 30 }}{ 5 } i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} -\frac{3}{x} &= \frac{5}{2}x&& \text{multiply ALL terms by } \color{blue}{ x\cdot2 }. \\[1 em]-x\cdot2\cdot\frac{3}{x} &= x\cdot2 \cdot \frac{5}{2}x&& \text{cancel out the denominators} \\[1 em]-6 &= 5x^2&& \text{move all terms to the left hand side } \\[1 em]-6-5x^2 &= 0&& \text{simplify left side} \\[1 em]-5x^2-6 &= 0&& \\[1 em] \end{aligned} $$
$ -5x^{2}-6 = 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