Question
$$x^2-10x+\frac{41}{2} = 0$$
Answer
$$ \begin{matrix}x_1 = 5-\dfrac{ 3 \sqrt{ 2}}{ 2 } & x_2 = 5+\dfrac{ 3 \sqrt{ 2}}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^2-10x+\frac{41}{2} &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2x^2-2\cdot10x+2\cdot\frac{41}{2} &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]2x^2-20x+41 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}-20x+41 = 0 $ is a quadratic equation.
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