Question
$$6x^2+7x-\frac{5}{3}x+5 = 0$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 4 }{ 9 }+\dfrac{\sqrt{ 206 }}{ 18 }i & x_2 = -\dfrac{ 4 }{ 9 }-\dfrac{\sqrt{ 206 }}{ 18 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 6x^2+7x-\frac{5}{3}x+5 &= 0&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot6x^2+3\cdot7x-3 \cdot \frac{5}{3}x+3\cdot5 &= 3\cdot0&& \text{cancel out the denominators} \\[1 em]18x^2+21x-5x+15 &= 0&& \text{simplify left side} \\[1 em]18x^2+16x+15 &= 0&& \\[1 em] \end{aligned} $$
$ 18x^{2}+16x+15 = 0 $ is a quadratic equation.
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