Vertical asymptotes happen at x=a if the function is undefined at x=a.
This is a rational functions, and rational functions are not defined when the denominator is zero, since you can't divide by zero.
In this case, the denominator is zero if
[tex]2x+3=0 \iff 2x=-3 \iff x=-\drac{3}{2}[/tex]
And thus the function has a vertical asymptote at x= -3/2
