Question
$$\frac{1}{2}x\cdot4x+2\cdot2x-2 = 0$$
Answer
$$ \begin{matrix}x_1 = -1-\sqrt{ 2 } & x_2 = -1+\sqrt{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{2}x\cdot4x+2\cdot2x-2 &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{1}{2}x\cdot4x+22\cdot2x-2\cdot2 &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]4x^2+8x-4 &= 0&& \\[1 em] \end{aligned} $$
$ 4x^{2}+8x-4 = 0 $ is a quadratic equation.
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