$$2x-3 = x^2$$
Answer
$$ \begin{matrix}x_1 = 1+\sqrt{ 2 }i & x_2 = 1-\sqrt{ 2 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 2x-3 &= x^2&& \text{move all terms to the left hand side } \\[1 em]2x-3-x^2 &= 0&& \text{simplify left side} \\[1 em]-x^2+2x-3 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+2x-3 = 0 $ is a quadratic equation.
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