Question
$$x^2+11 \cdot \frac{x}{3} = \frac{5}{12}$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 11 }{ 6 }-\dfrac{\sqrt{ 34 }}{ 3 } & x_2 = -\dfrac{ 11 }{ 6 }+\dfrac{\sqrt{ 34 }}{ 3 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^2+11 \cdot \frac{x}{3} &= \frac{5}{12}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12x^2+12\cdot11 \cdot \frac{x}{3} &= 12\cdot\frac{5}{12}&& \text{cancel out the denominators} \\[1 em]12x^2+44x &= 5&& \text{move all terms to the left hand side } \\[1 em]12x^2+44x-5 &= 0&& \\[1 em] \end{aligned} $$
$ 12x^{2}+44x-5 = 0 $ is a quadratic equation.
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