Question
$$(2x-1)x = 100$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 1 }{ 4 }-\dfrac{ 3 \sqrt{ 89}}{ 4 } & x_2 = \dfrac{ 1 }{ 4 }+\dfrac{ 3 \sqrt{ 89}}{ 4 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (2x-1)x &= 100&& \text{simplify left side} \\[1 em]2x^2-x &= 100&& \text{move all terms to the left hand side } \\[1 em]2x^2-x-100 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}-x-100 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
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