$$ \begin{aligned} \frac{3}{4}x+4 &= \frac{1}{4}x-9&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{3}{4}x+4\cdot4 &= 4 \cdot \frac{1}{4}x-4\cdot9&& \text{cancel out the denominators} \\[1 em]3x+16 &= x-36&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ 16 }$ to the right} \\[1 em]3x-x &= -36-16&& \text{simplify left and right hand side} \\[1 em]2x &= -52&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= -\frac{52}{2}&& \\[1 em]x &= -26&& \\[1 em] \end{aligned} $$

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