Question
$$x = \frac{100\cdot10+x\cdot5}{x+100}$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 95 }{ 2 }-\dfrac{ 5 \sqrt{ 521}}{ 2 } & x_2 = -\dfrac{ 95 }{ 2 }+\dfrac{ 5 \sqrt{ 521}}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x &= \frac{100\cdot10+x\cdot5}{x+100}&& \text{multiply ALL terms by } \color{blue}{ x+100 }. \\[1 em](x+100)x &= (x+100)\frac{100\cdot10+x\cdot5}{x+100}&& \text{cancel out the denominators} \\[1 em]x^2+100x &= 1000+5x&& \text{move all terms to the left hand side } \\[1 em]x^2+100x-1000-5x &= 0&& \text{simplify left side} \\[1 em]x^2+95x-1000 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}+95x-1000 = 0 $ is a quadratic equation.
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