$$\frac{7}{4x}-\frac{3}{x^2} = \frac{1}{2x^2}$$

$$ \begin{aligned} \frac{7}{4x}-\frac{3}{x^2} &= \frac{1}{2x^2}&& \text{multiply ALL terms by } \color{blue}{ 4xx^2\cdot2 }. \\[1 em]4xx^2\cdot2\cdot\frac{7}{4x}-4xx^2\cdot2\cdot\frac{3}{x^2} &= 4xx^2\cdot2\cdot\frac{1}{2x^2}&& \text{cancel out the denominators} \\[1 em]14-\frac{24}{x^1} &= 4x&& \text{multiply ALL terms by } \color{blue}{ x^1 }. \\[1 em]x^1\cdot14-x^1\cdot\frac{24}{x^1} &= x^1\cdot4x&& \text{cancel out the denominators} \\[1 em]14x-24 &= 4x^2&& \text{move all terms to the left hand side } \\[1 em]14x-24-4x^2 &= 0&& \text{simplify left side} \\[1 em]-4x^2+14x-24 &= 0&& \\[1 em] \end{aligned} $$

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