Question
$$\frac{5}{9}x\cdot9x\cdot7-10 = 0$$
Answer
$$ \begin{matrix}x_1 = - \dfrac{\sqrt{ 14 }}{ 7 } & x_2 = \dfrac{\sqrt{ 14 }}{ 7 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{5}{9}x\cdot9x\cdot7-10 &= 0&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]9 \cdot \frac{5}{9}x\cdot9x\cdot7-9\cdot10 &= 9\cdot0&& \text{cancel out the denominators} \\[1 em]315x^2-90 &= 0&& \\[1 em] \end{aligned} $$
$ 315x^{2}-90 = 0 $ is a quadratic equation.
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