Question
$$x(x+6) = 47$$
Answer
$$ \begin{matrix}x_1 = -3-2 \sqrt{ 14 } & x_2 = -3+2 \sqrt{ 14 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x(x+6) &= 47&& \text{simplify left side} \\[1 em]x^2+6x &= 47&& \text{move all terms to the left hand side } \\[1 em]x^2+6x-47 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}+6x-47 = 0 $ is a quadratic equation.
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