Question
$$\frac{7}{5x-2} = \frac{3}{4x}$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = \dfrac{ 1 }{ 5 }-\dfrac{\sqrt{ 429 }}{ 15 } & x_3 = \dfrac{ 1 }{ 5 }+\dfrac{\sqrt{ 429 }}{ 15 } \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{7}{5x-2} &= \frac{3}{4x}&& \text{multiply ALL terms by } \color{blue}{ (5x-2)\cdot4x }. \\[1 em](5x-2)\cdot4x\cdot\frac{7}{5x-2} &= (5x-2)\cdot4x\cdot\frac{3}{4x}&& \text{cancel out the denominators} \\[1 em]28x &= 15x^3-6x^2&& \text{move all terms to the left hand side } \\[1 em]28x-15x^3+6x^2 &= 0&& \text{simplify left side} \\[1 em]-15x^3+6x^2+28x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ -15x^{3}+6x^{2}+28x = 0 } $, first we need to factor our $ x $.
$$ -15x^{3}+6x^{2}+28x = x \left( -15x^{2}+6x+28 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ -15x^{2}+6x+28 = 0$.
$ -15x^{2}+6x+28 = 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