An equation is shown below:
3/2x + 7/2 = 2^x
x = 1
x = 3
x = 5
x = 8

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If you're supposed to find x that satisfies this equation, this is a relatively challenging problem.  

One way to approximate the solution would be to plot y = (3/2)x + 7/2  and  y=2^x carefully on the same set of axes.  Try to read off the x- and y-values at the single point where these two graphs intersect.   (x, y) would be your solution.  

I did this graphically on my calculator and found that the point of intersection is (3,8).

To check, determine whether y = 2^x is true when x = 3 and y = 8, and also check whether   y = (3/2)x + 7/2   is true for the same x and y values.