$$ \begin{aligned} 8-\frac{1}{4}x &= \frac{2}{5}x+14&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20\cdot8-20 \cdot \frac{1}{4}x &= 20 \cdot \frac{2}{5}x+20\cdot14&& \text{cancel out the denominators} \\[1 em]160-5x &= 8x+280&& \text{move the $ \color{blue}{ 8x } $ to the left side and $ \color{blue}{ 160 }$ to the right} \\[1 em]-5x-8x &= 280-160&& \text{simplify left and right hand side} \\[1 em]-13x &= 120&& \text{ divide both sides by $ -13 $ } \\[1 em]x &= -\frac{120}{13}&& \\[1 em] \end{aligned} $$

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