Question
$$\frac{4}{3}x+\frac{5}{4} = \frac{3}{x}$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 15 }{ 32 }-\dfrac{ 3 \sqrt{ 281}}{ 32 } & x_2 = -\dfrac{ 15 }{ 32 }+\dfrac{ 3 \sqrt{ 281}}{ 32 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{4}{3}x+\frac{5}{4} &= \frac{3}{x}&& \text{multiply ALL terms by } \color{blue}{ 3\cdot4x }. \\[1 em]3\cdot4x \cdot \frac{4}{3}x+3\cdot4x\cdot\frac{5}{4} &= 3\cdot4x\cdot\frac{3}{x}&& \text{cancel out the denominators} \\[1 em]16x^2+15x &= 36&& \text{move all terms to the left hand side } \\[1 em]16x^2+15x-36 &= 0&& \\[1 em] \end{aligned} $$
$ 16x^{2}+15x-36 = 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