$$ \begin{aligned} 2x-\frac{3}{4}x+\frac{5}{2} &= 0&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4\cdot2x-4 \cdot \frac{3}{4}x+4\cdot\frac{5}{2} &= 4\cdot0&& \text{cancel out the denominators} \\[1 em]8x-3x+10 &= 0&& \text{simplify left side} \\[1 em]5x+10 &= 0&& \text{ move the constants to the right } \\[1 em]5x &= -10&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= -\frac{10}{5}&& \\[1 em]x &= -2&& \\[1 em] \end{aligned} $$

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