Question
$$2 \cdot \frac{x^2}{4}-\frac{x}{6} = \frac{3}{2}$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 1 }{ 6 }-\dfrac{\sqrt{ 109 }}{ 6 } & x_2 = \dfrac{ 1 }{ 6 }+\dfrac{\sqrt{ 109 }}{ 6 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 2 \cdot \frac{x^2}{4}-\frac{x}{6} &= \frac{3}{2}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12\cdot2 \cdot \frac{x^2}{4}-12\frac{x}{6} &= 12\cdot\frac{3}{2}&& \text{cancel out the denominators} \\[1 em]6x^2-2x &= 18&& \text{move all terms to the left hand side } \\[1 em]6x^2-2x-18 &= 0&& \\[1 em] \end{aligned} $$
$ 6x^{2}-2x-18 = 0 $ is a quadratic equation.
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