Question
$$x^2+\frac{6}{10}+9 = 0$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 4 \sqrt{ 15}}{ 5 } i & x_2 = -4 \dfrac{\sqrt{ 15 }}{ 5 } i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^2+\frac{6}{10}+9 &= 0&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10x^2+10\cdot\frac{6}{10}+10\cdot9 &= 10\cdot0&& \text{cancel out the denominators} \\[1 em]10x^2+6+90 &= 0&& \text{simplify left side} \\[1 em]10x^2+96 &= 0&& \\[1 em] \end{aligned} $$
$ 10x^{2}+96 = 0 $ is a quadratic equation.
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