$$21 = \frac{1}{2}(x+1)x$$
Answer
$$ \begin{matrix}x_1 = 6 & x_2 = -7 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 21 &= \frac{1}{2}(x+1)x&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot21 &= 2 \cdot \frac{1}{2}(x+1)x&& \text{cancel out the denominators} \\[1 em]42 &= x^2+x&& \text{move all terms to the left hand side } \\[1 em]42-x^2-x &= 0&& \text{simplify left side} \\[1 em]-x^2-x+42 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}-x+42 = 0 $ is a quadratic equation.
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