$$ \begin{aligned} \frac{m}{2}-\frac{3}{4} &= \frac{5}{6}-\frac{m}{18}&& \text{multiply ALL terms by } \color{blue}{ 36 }. \\[1 em]36 \cdot \frac{m}{2}-36\cdot\frac{3}{4} &= 36\cdot\frac{5}{6}-36\frac{m}{18}&& \text{cancel out the denominators} \\[1 em]18m-27 &= 30-2m&& \text{move the $ \color{blue}{ -2m } $ to the left side and $ \color{blue}{ -27 }$ to the right} \\[1 em]18m+2m &= 30+27&& \text{simplify left and right hand side} \\[1 em]20m &= 57&& \text{ divide both sides by $ 20 $ } \\[1 em]m &= \frac{57}{20}&& \\[1 em] \end{aligned} $$

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