Question
$$\frac{4}{3}x-\frac{1}{x} = x+\frac{2}{2}x^2$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 3 }{ 2 }-\dfrac{\sqrt{ 21 }}{ 2 } & x_2 = \dfrac{ 3 }{ 2 }+\dfrac{\sqrt{ 21 }}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{4}{3}x-\frac{1}{x} &= x+\frac{2}{2}x^2&& \text{multiply ALL terms by } \color{blue}{ 3x\cdot2 }. \\[1 em]3x\cdot2 \cdot \frac{4}{3}x-3x\cdot2\cdot\frac{1}{x} &= 3x\cdot2x+3x\cdot2 \cdot \frac{2}{2}x^2&& \text{cancel out the denominators} \\[1 em]8x^2-6 &= 6x^2+6x&& \text{move all terms to the left hand side } \\[1 em]8x^2-6-6x^2-6x &= 0&& \text{simplify left side} \\[1 em]2x^2-6x-6 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}-6x-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