Question
$$18x(\frac{2}{9}x-\frac{1}{2}) = 3$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 9 }{ 8 }-\dfrac{\sqrt{ 129 }}{ 8 } & x_2 = \dfrac{ 9 }{ 8 }+\dfrac{\sqrt{ 129 }}{ 8 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 18x(\frac{2}{9}x-\frac{1}{2}) &= 3&& \text{simplify left side} \\[1 em]18x(\frac{2x}{9}-\frac{1}{2}) &= 3&& \\[1 em]18x \cdot \frac{4x-9}{18} &= 3&& \\[1 em]\frac{72x^2-162x}{18} &= 3&& \text{multiply ALL terms by } \color{blue}{ 18 }. \\[1 em]18 \cdot \frac{72x^2-162x}{18} &= 18\cdot3&& \text{cancel out the denominators} \\[1 em]72x^2-162x &= 54&& \text{move all terms to the left hand side } \\[1 em]72x^2-162x-54 &= 0&& \\[1 em] \end{aligned} $$
$ 72x^{2}-162x-54 = 0 $ is a quadratic equation.
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