$$\frac{1}{5x}-\frac{7}{5} = \frac{4}{9x}$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = -\dfrac{ 63 }{ 11 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{5x}-\frac{7}{5} &= \frac{4}{9x}&& \text{multiply ALL terms by } \color{blue}{ 5x\cdot9 }. \\[1 em]5x\cdot9\cdot\frac{1}{5x}-5x\cdot9\cdot\frac{7}{5} &= 5x\cdot9\cdot\frac{4}{9x}&& \text{cancel out the denominators} \\[1 em]9x^2-63x &= 20x^2&& \text{move all terms to the left hand side } \\[1 em]9x^2-63x-20x^2 &= 0&& \text{simplify left side} \\[1 em]-11x^2-63x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ -11x^{2}-63x = 0 } $, first we need to factor our $ x $.
$$ -11x^{2}-63x = x \left( -11x-63 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The second root can be found by solving equation $ -11x-63 = 0$.
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