Question
$$7 = \frac{1}{4}x(3x-12)$$
Answer
$$ \begin{matrix}x_1 = 2-\dfrac{ 2 \sqrt{ 30}}{ 3 } & x_2 = 2+\dfrac{ 2 \sqrt{ 30}}{ 3 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 7 &= \frac{1}{4}x(3x-12)&& \text{simplify right side} \\[1 em]7 &= \frac{x}{4}(3x-12)&& \\[1 em]7 &= \frac{3x^2-12x}{4}&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4\cdot7 &= 4 \cdot \frac{3x^2-12x}{4}&& \text{cancel out the denominators} \\[1 em]28 &= 3x^2-12x&& \text{move all terms to the left hand side } \\[1 em]28-3x^2+12x &= 0&& \text{simplify left side} \\[1 em]-3x^2+12x+28 &= 0&& \\[1 em] \end{aligned} $$
$ -3x^{2}+12x+28 = 0 $ is a quadratic equation.
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