Question
$$x+(100-x)\frac{x}{100}+x = 100$$
Answer
$$ \begin{matrix}x_1 = 150-50 \sqrt{ 5 } & x_2 = 150+50 \sqrt{ 5 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x+(100-x)\frac{x}{100}+x &= 100&& \text{multiply ALL terms by } \color{blue}{ 100 }. \\[1 em]100x+100(100-x)\frac{x}{100}+100x &= 100\cdot100&& \text{cancel out the denominators} \\[1 em]100x-x^2+100x+100x &= 10000&& \text{simplify left side} \\[1 em]-x^2+200x+100x &= 10000&& \\[1 em]-x^2+300x &= 10000&& \text{move all terms to the left hand side } \\[1 em]-x^2+300x-10000 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+300x-10000 = 0 $ is a quadratic equation.
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