$$\frac{x^2+2x+6}{x-3} = 0$$
Answer
$$ \begin{matrix}x_1 = -1+\sqrt{ 5 }i & x_2 = -1-\sqrt{ 5 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{x^2+2x+6}{x-3} &= 0&& \text{multiply ALL terms by } \color{blue}{ x-3 }. \\[1 em](x-3)\frac{x^2+2x+6}{x-3} &= (x-3)\cdot0&& \text{cancel out the denominators} \\[1 em]x^2+2x+6 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}+2x+6 = 0 $ is a quadratic equation.
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