$$ \begin{aligned} 0 &= -x^2+2x+3&& \text{move all terms to the left hand side } \\[1 em]0+x^2-2x-3 &= 0&& \text{simplify left side} \\[1 em]x^2-2x-3 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}-2x-3 = 0 $ is a quadratic equation.
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