$$ \begin{aligned} \frac{5}{x} &= \frac{8}{2x-6}&& \text{multiply ALL terms by } \color{blue}{ x(2x-6) }. \\[1 em]x(2x-6)\cdot\frac{5}{x} &= x(2x-6)\cdot\frac{8}{2x-6}&& \text{cancel out the denominators} \\[1 em]10x-30 &= 8x&& \text{move the $ \color{blue}{ 8x } $ to the left side and $ \color{blue}{ -30 }$ to the right} \\[1 em]10x-8x &= 30&& \text{simplify left side} \\[1 em]2x &= 30&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{30}{2}&& \\[1 em]x &= 15&& \\[1 em] \end{aligned} $$

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