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