Answer
$$x=\frac{2a+3b}{a-2b}, \quad (a \neq 2b)$$
Work Step by Step
$$a(x-2)=b(2x+3) \quad \Rightarrow \quad ax-2a=2bx+3b \quad \Rightarrow \quad (a-2b) x=2a+3b \quad \Rightarrow \quad x= \frac{2a+3b}{a-2b}, \quad (a \neq 2b)$$
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