Question
$$6x-\frac{27}{4}-x^2 = 0$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 3 }{ 2 } & x_2 = \dfrac{ 9 }{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 6x-\frac{27}{4}-x^2 &= 0&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4\cdot6x-4\cdot\frac{27}{4}-4x^2 &= 4\cdot0&& \text{cancel out the denominators} \\[1 em]24x-27-4x^2 &= 0&& \text{simplify left side} \\[1 em]-4x^2+24x-27 &= 0&& \\[1 em] \end{aligned} $$
$ -4x^{2}+24x-27 = 0 $ is a quadratic equation.
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