Question
$$\frac{4}{x}+\frac{9}{7} = \frac{1}{7}x$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 9 }{ 2 }-\dfrac{\sqrt{ 193 }}{ 2 } & x_2 = \dfrac{ 9 }{ 2 }+\dfrac{\sqrt{ 193 }}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{4}{x}+\frac{9}{7} &= \frac{1}{7}x&& \text{multiply ALL terms by } \color{blue}{ x\cdot7 }. \\[1 em]x\cdot7\cdot\frac{4}{x}+x\cdot7\cdot\frac{9}{7} &= x\cdot7 \cdot \frac{1}{7}x&& \text{cancel out the denominators} \\[1 em]28+9x &= x^2&& \text{move all terms to the left hand side } \\[1 em]28+9x-x^2 &= 0&& \text{simplify left side} \\[1 em]-x^2+9x+28 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+9x+28 = 0 $ is a quadratic equation.
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