$$\frac{9}{4} = 7x+\frac{6}{x-2}$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 65 }{ 56 }+\dfrac{\sqrt{ 479 }}{ 56 }i & x_2 = \dfrac{ 65 }{ 56 }-\dfrac{\sqrt{ 479 }}{ 56 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{9}{4} &= 7x+\frac{6}{x-2}&& \text{multiply ALL terms by } \color{blue}{ 4(x-2) }. \\[1 em]4(x-2)\cdot\frac{9}{4} &= 4(x-2)\cdot7x+4(x-2)\cdot\frac{6}{x-2}&& \text{cancel out the denominators} \\[1 em]9x-18 &= 28x^2-56x+24&& \text{move all terms to the left hand side } \\[1 em]9x-18-28x^2+56x-24 &= 0&& \text{simplify left side} \\[1 em]-28x^2+65x-42 &= 0&& \\[1 em] \end{aligned} $$
$ -28x^{2}+65x-42 = 0 $ is a quadratic equation.
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