$$x \cdot \frac{x+1}{2} = 100$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 1 }{ 2 }-\dfrac{ 3 \sqrt{ 89}}{ 2 } & x_2 = -\dfrac{ 1 }{ 2 }+\dfrac{ 3 \sqrt{ 89}}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x \cdot \frac{x+1}{2} &= 100&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2x \cdot \frac{x+1}{2} &= 2\cdot100&& \text{cancel out the denominators} \\[1 em]x^2+x &= 200&& \text{move all terms to the left hand side } \\[1 em]x^2+x-200 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}+x-200 = 0 $ is a quadratic equation.
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