Question
$$\frac{7}{3}x = \frac{2}{x+5}$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 5 }{ 2 }-\dfrac{\sqrt{ 1393 }}{ 14 } & x_2 = -\dfrac{ 5 }{ 2 }+\dfrac{\sqrt{ 1393 }}{ 14 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{7}{3}x &= \frac{2}{x+5}&& \text{multiply ALL terms by } \color{blue}{ 3(x+5) }. \\[1 em]3(x+5)\frac{7}{3}x &= 3(x+5)\cdot\frac{2}{x+5}&& \text{cancel out the denominators} \\[1 em]7x^2+35x &= 6&& \text{move all terms to the left hand side } \\[1 em]7x^2+35x-6 &= 0&& \\[1 em] \end{aligned} $$
$ 7x^{2}+35x-6 = 0 $ is a quadratic equation.
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