$$\frac{3}{4x-5} = x$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 5 }{ 8 }-\dfrac{\sqrt{ 73 }}{ 8 } & x_2 = \dfrac{ 5 }{ 8 }+\dfrac{\sqrt{ 73 }}{ 8 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{3}{4x-5} &= x&& \text{multiply ALL terms by } \color{blue}{ 4x-5 }. \\[1 em](4x-5)\cdot\frac{3}{4x-5} &= (4x-5)x&& \text{cancel out the denominators} \\[1 em]3 &= 4x^2-5x&& \text{move all terms to the left hand side } \\[1 em]3-4x^2+5x &= 0&& \text{simplify left side} \\[1 em]-4x^2+5x+3 &= 0&& \\[1 em] \end{aligned} $$
$ -4x^{2}+5x+3 = 0 $ is a quadratic equation.
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