Question
$$-\frac{1}{4}x^2+3x+1 = 0$$
Answer
$$ \begin{matrix}x_1 = 6-2 \sqrt{ 10 } & x_2 = 6+2 \sqrt{ 10 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} -\frac{1}{4}x^2+3x+1 &= 0&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]-4 \cdot \frac{1}{4}x^2+4\cdot3x+4\cdot1 &= 4\cdot0&& \text{cancel out the denominators} \\[1 em]-x^2+12x+4 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+12x+4 = 0 $ is a quadratic equation.
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