Question
$$\frac{3}{2}x-1+\frac{1}{x}+4 = 5x+\frac{11}{2}x^2+7x+4$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 13 }{ 42 }-\dfrac{\sqrt{ 337 }}{ 42 } & x_2 = -\dfrac{ 13 }{ 42 }+\dfrac{\sqrt{ 337 }}{ 42 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{3}{2}x-1+\frac{1}{x}+4 &= 5x+\frac{11}{2}x^2+7x+4&& \text{multiply ALL terms by } \color{blue}{ 2x }. \\[1 em]2x \cdot \frac{3}{2}x-2x\cdot1+2x\cdot\frac{1}{x}+2x\cdot4 &= 2x\cdot5x+2x \cdot \frac{11}{2}x^2+2x\cdot7x+2x\cdot4&& \text{cancel out the denominators} \\[1 em]3x^2-2x+2+8x &= 10x^2+11x+14x^2+8x&& \text{simplify left and right hand side} \\[1 em]3x^2+6x+2 &= 24x^2+19x&& \text{move all terms to the left hand side } \\[1 em]3x^2+6x+2-24x^2-19x &= 0&& \text{simplify left side} \\[1 em]-21x^2-13x+2 &= 0&& \\[1 em] \end{aligned} $$
$ -21x^{2}-13x+2 = 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