$$5+\frac{1}{2-3x} = 5x$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 5 }{ 6 }+\dfrac{\sqrt{ 35 }}{ 30 }i & x_2 = \dfrac{ 5 }{ 6 }-\dfrac{\sqrt{ 35 }}{ 30 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 5+\frac{1}{2-3x} &= 5x&& \text{multiply ALL terms by } \color{blue}{ 2-3x }. \\[1 em](2-3x)\cdot5+(2-3x)\cdot\frac{1}{2-3x} &= (2-3x)\cdot5x&& \text{cancel out the denominators} \\[1 em]-15x+10+1 &= -15x^2+10x&& \text{simplify left side} \\[1 em]-15x+11 &= -15x^2+10x&& \text{move all terms to the left hand side } \\[1 em]-15x+11+15x^2-10x &= 0&& \text{simplify left side} \\[1 em]15x^2-25x+11 &= 0&& \\[1 em] \end{aligned} $$
$ 15x^{2}-25x+11 = 0 $ is a quadratic equation.
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