$$s+\frac{5}{s} = -6$$
Answer
$$ \begin{matrix}s_1 = -1 & s_2 = -5 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} s+\frac{5}{s} &= -6&& \text{multiply ALL terms by } \color{blue}{ s }. \\[1 em]ss+s\cdot\frac{5}{s} &= s\cdot(-6)&& \text{cancel out the denominators} \\[1 em]s^2+5 &= -6s&& \text{move all terms to the left hand side } \\[1 em]s^2+5+6s &= 0&& \text{simplify left side} \\[1 em]s^2+6s+5 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}+6x+5 = 0 $ is a quadratic equation.
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