Question
$$2x+5 \cdot \frac{x}{x}+4 = x+\frac{2}{x}+4$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 5 }{ 2 }-\dfrac{\sqrt{ 33 }}{ 2 } & x_2 = -\dfrac{ 5 }{ 2 }+\dfrac{\sqrt{ 33 }}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 2x+5 \cdot \frac{x}{x}+4 &= x+\frac{2}{x}+4&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot2x+x\cdot5 \cdot \frac{x}{x}+x\cdot4 &= xx+x\cdot\frac{2}{x}+x\cdot4&& \text{cancel out the denominators} \\[1 em]2x^2+5x+4x &= x^2+2+4x&& \text{simplify left and right hand side} \\[1 em]2x^2+9x &= x^2+4x+2&& \text{move all terms to the left hand side } \\[1 em]2x^2+9x-x^2-4x-2 &= 0&& \text{simplify left side} \\[1 em]x^2+5x-2 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}+5x-2 = 0 $ is a quadratic equation.
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