Question
$$(x+6)^2 = \frac{x}{3}$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 35 }{ 6 }+\dfrac{\sqrt{ 71 }}{ 6 }i & x_2 = -\dfrac{ 35 }{ 6 }-\dfrac{\sqrt{ 71 }}{ 6 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (x+6)^2 &= \frac{x}{3}&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3(x+6)^2 &= 3 \cdot \frac{x}{3}&& \text{cancel out the denominators} \\[1 em]3(x+6)^2 &= x&& \text{simplify left side} \\[1 em]3(x^2+12x+36) &= x&& \\[1 em]3x^2+36x+108 &= x&& \text{move all terms to the left hand side } \\[1 em]3x^2+36x+108-x &= 0&& \text{simplify left side} \\[1 em]3x^2+35x+108 &= 0&& \\[1 em] \end{aligned} $$
$ 3x^{2}+35x+108 = 0 $ is a quadratic equation.
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