$$80 = x+x^2+2+x^2$$
Answer
$$ \begin{matrix}x_1 = 6 & x_2 = -\dfrac{ 13 }{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 80 &= x+x^2+2+x^2&& \text{simplify right side} \\[1 em]80 &= 2x^2+x+2&& \text{move all terms to the left hand side } \\[1 em]80-2x^2-x-2 &= 0&& \text{simplify left side} \\[1 em]-2x^2-x+78 &= 0&& \\[1 em] \end{aligned} $$
$ -2x^{2}-x+78 = 0 $ is a quadratic equation.
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