$$ \begin{aligned} (-\frac{1}{9})x^2+\frac{2}{3}x+10 &= 0&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]9(-\frac{1}{9})x^2+9\frac{2}{3}x+9\cdot10 &= 9\cdot0&& \text{cancel out the denominators} \\[1 em]0+6x+90 &= 0&& \text{simplify left side} \\[1 em]6x+90 &= 0&& \text{ move the constants to the right } \\[1 em]6x &= -90&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= -\frac{90}{6}&& \\[1 em]x &= -15&& \\[1 em] \end{aligned} $$

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