$$5-\frac{r}{4} = \frac{1}{r}$$
Answer
$$ \begin{matrix}r_1 = 10-4 \sqrt{ 6 } & r_2 = 10+4 \sqrt{ 6 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 5-\frac{r}{4} &= \frac{1}{r}&& \text{multiply ALL terms by } \color{blue}{ 4r }. \\[1 em]4r\cdot5-4r\frac{r}{4} &= 4r\cdot\frac{1}{r}&& \text{cancel out the denominators} \\[1 em]20r-r^2 &= 4&& \text{simplify left side} \\[1 em]-r^2+20r &= 4&& \text{move all terms to the left hand side } \\[1 em]-r^2+20r-4 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+20x-4 = 0 $ is a quadratic equation.
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