Question
$$4x-\frac{9}{x} = -9$$
Answer
$$ \begin{matrix}x_1 = -3 & x_2 = \dfrac{ 3 }{ 4 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 4x-\frac{9}{x} &= -9&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot4x-x\cdot\frac{9}{x} &= x\cdot(-9)&& \text{cancel out the denominators} \\[1 em]4x^2-9 &= -9x&& \text{move all terms to the left hand side } \\[1 em]4x^2-9+9x &= 0&& \text{simplify left side} \\[1 em]4x^2+9x-9 &= 0&& \\[1 em] \end{aligned} $$
$ 4x^{2}+9x-9 = 0 $ is a quadratic equation.
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