If the final image of the object O coincides with it then the sum of all possible values of x is

Only two value of x are possible.

When the image from the spherical surface forms at infinite(light rays retraces) and when the image from the spherical surface forms at the same point as object.
$\frac{3}{2\left(\infty \right)}-\frac{1}{-x_1}=\frac{\left(\frac{3}{2}-1\right)}{R}$

 
 
So,