Question
$$\frac{3}{x}+\frac{3}{2}x+\frac{1}{2} = 0$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 1 }{ 6 }+\dfrac{\sqrt{ 71 }}{ 6 }i & x_2 = -\dfrac{ 1 }{ 6 }-\dfrac{\sqrt{ 71 }}{ 6 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{3}{x}+\frac{3}{2}x+\frac{1}{2} &= 0&& \text{multiply ALL terms by } \color{blue}{ x\cdot2 }. \\[1 em]x\cdot2\cdot\frac{3}{x}+x\cdot2\frac{3}{2}x+x\cdot2\cdot\frac{1}{2} &= x\cdot2\cdot0&& \text{cancel out the denominators} \\[1 em]6+3x^2+x &= 0&& \text{simplify left side} \\[1 em]3x^2+x+6 &= 0&& \\[1 em] \end{aligned} $$
$ 3x^{2}+x+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