$$\frac{400}{x}+\frac{400}{x+5} = 4$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 195 }{ 2 }-\dfrac{ 5 \sqrt{ 1601}}{ 2 } & x_2 = \dfrac{ 195 }{ 2 }+\dfrac{ 5 \sqrt{ 1601}}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{400}{x}+\frac{400}{x+5} &= 4&& \text{multiply ALL terms by } \color{blue}{ x(x+5) }. \\[1 em]x(x+5)\cdot\frac{400}{x}+x(x+5)\cdot\frac{400}{x+5} &= x(x+5)\cdot4&& \text{cancel out the denominators} \\[1 em]400x+2000+400x &= 4x^2+20x&& \text{simplify left side} \\[1 em]800x+2000 &= 4x^2+20x&& \text{move all terms to the left hand side } \\[1 em]800x+2000-4x^2-20x &= 0&& \text{simplify left side} \\[1 em]-4x^2+780x+2000 &= 0&& \\[1 em] \end{aligned} $$
$ -4x^{2}+780x+2000 = 0 $ is a quadratic equation.
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