$$x^2-2x+\frac{5}{2} = 0$$
Answer
$$ \begin{matrix}x_1 = 1+\dfrac{\sqrt{ 6 }}{ 2 }i & x_2 = 1-\dfrac{\sqrt{ 6 }}{ 2 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^2-2x+\frac{5}{2} &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2x^2-2\cdot2x+2\cdot\frac{5}{2} &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]2x^2-4x+5 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}-4x+5 = 0 $ is a quadratic equation.
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