To solve the equation, we need to simplify it step by step:

3/x + 2 - $3/2-x$ = 2/x^2 - 4

First, simplify the fractions:

3/x + 2 - $3/2$ + x = 2/x^2 - 4

Next, combine like terms:

$3/x+x$ - $3/2$ = 2/x^2 - 2

Now, get a common denominator and combine terms:

$3x+x^2$/x - 3/2 = 2/x^2 - 2

Now, multiply both sides by x to get rid of the denominator:

3x + x^2 - 3x/2 = 2 - 2x

Simplify further:

2x + x^2/2 = 2 - 2x

Multiply through by 2 to clear the fraction:

4x + x^2 = 4 - 4x

Rearrange the equation to set it equal to 0:

x^2 + 8x - 4 = 0

Now we have a quadratic equation which can be solved using the quadratic formula:

x = $-b\pm \surd (b^2-4ac)$/2a

Plugging in the values for a, b, and c:

x = $-8\pm \surd (64+16)$/2
x = $-8\pm \surd 80$/2
x = $-8\pm 4\surd 5$/2
x = -4 ± 2√5

Therefore, the solutions to the equation are:

x = -4 + 2√5
x = -4 - 2√5