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