Question
$$-\frac{1}{9}x^2+\frac{6}{9}x-\frac{1}{2} = 0$$
Answer
$$ \begin{matrix}x_1 = 3-\dfrac{ 3 \sqrt{ 2}}{ 2 } & x_2 = 3+\dfrac{ 3 \sqrt{ 2}}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} -\frac{1}{9}x^2+\frac{6}{9}x-\frac{1}{2} &= 0&& \text{multiply ALL terms by } \color{blue}{ 18 }. \\[1 em]-18 \cdot \frac{1}{9}x^2+18\frac{6}{9}x-18\cdot\frac{1}{2} &= 18\cdot0&& \text{cancel out the denominators} \\[1 em]-2x^2+12x-9 &= 0&& \\[1 em] \end{aligned} $$
$ -2x^{2}+12x-9 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
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