To find the values of x1 and x2, we can set up a system of equations using the given information:

1) x1 + x2 = -3/2
2) x1 * x2 = -2

Now, we can use the substitution method to solve the system. Let's solve for x1 in terms of x2 using equation 1:

x1 = -3/2 - x2

Now, substitute x1 into equation 2:

(-3/2 - x2) x2 = -2
-3/2x2 - x2^2 = -2
-x2^2 - 3/2*x2 + 2 = 0

This is a quadratic equation. We can now use the quadratic formula to solve for x2:

x2 = [3/2 ± sqrt((3/2)^2 - 4(-1)2)] / (-2)
x2 = [3/2 ± sqrt(9/4 + 8)] / (-2)
x2 = [3/2 ± sqrt(25/4)] / (-2)
x2 = [3/2 ± 5/2] / (-2)
So, x2 = 4 or x2 = -2

Now, we can find the corresponding values of x1:

For x2 = 4:
x1 = -3/2 - 4 = -11/2

For x2 = -2:
x1 = -3/2 - (-2) = 1/2

Therefore, the solutions to the system of equations are x1 = -11/2, x2 = 4 and x1 = 1/2, x2 = -2.