$$\frac{1}{t-2} = \frac{t}{8}$$
Answer
$$ \begin{matrix}t_1 = -2 & t_2 = 4 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{t-2} &= \frac{t}{8}&& \text{multiply ALL terms by } \color{blue}{ (t-2)\cdot8 }. \\[1 em](t-2)\cdot8\cdot\frac{1}{t-2} &= (t-2)\cdot8 \cdot \frac{t}{8}&& \text{cancel out the denominators} \\[1 em]8 &= t^2-2t&& \text{move all terms to the left hand side } \\[1 em]8-t^2+2t &= 0&& \text{simplify left side} \\[1 em]-t^2+2t+8 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+2x+8 = 0 $ is a quadratic equation.
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