Question
$$0 = x^2\cdot50+x\cdot50-\frac{1}{4}\cdot50$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 1 }{ 2 }-\dfrac{\sqrt{ 2 }}{ 2 } & x_2 = -\dfrac{ 1 }{ 2 }+\dfrac{\sqrt{ 2 }}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 0 &= x^2\cdot50+x\cdot50-\frac{1}{4}\cdot50&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4\cdot0 &= 4x^2\cdot50+4x\cdot50-4 \cdot \frac{1}{4}\cdot50&& \text{cancel out the denominators} \\[1 em]0 &= 200x^2+200x-50&& \text{move all terms to the left hand side } \\[1 em]0-200x^2-200x+50 &= 0&& \text{simplify left side} \\[1 em]-200x^2-200x+50 &= 0&& \\[1 em] \end{aligned} $$
$ -200x^{2}-200x+50 = 0 $ is a quadratic equation.
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