$$x-\frac{3}{x} = \frac{9}{10}$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 9 }{ 20 }-\dfrac{\sqrt{ 1281 }}{ 20 } & x_2 = \dfrac{ 9 }{ 20 }+\dfrac{\sqrt{ 1281 }}{ 20 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x-\frac{3}{x} &= \frac{9}{10}&& \text{multiply ALL terms by } \color{blue}{ x\cdot10 }. \\[1 em]x\cdot10x-x\cdot10\cdot\frac{3}{x} &= x\cdot10\cdot\frac{9}{10}&& \text{cancel out the denominators} \\[1 em]10x^2-30 &= 9x&& \text{move all terms to the left hand side } \\[1 em]10x^2-30-9x &= 0&& \text{simplify left side} \\[1 em]10x^2-9x-30 &= 0&& \\[1 em] \end{aligned} $$
$ 10x^{2}-9x-30 = 0 $ is a quadratic equation.
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