We can start by solving for x in the given equation:
x + 1/2 = 5
x = 5 - 1/2
x = 9/2
Now, we can substitute this value of x into the expression 2*x^2 - 3x + 6 - 3/x +2/x^2:
2*(9/2)^2 - 3*(9/2) + 6 - 3/(9/2) + 2/(9/2)^2
Simplifying each term, we get:
2*(81/4) - 27/2 + 6 - 6/9 + 2/(81/4)
81/2 - 27/2 + 6 - 2/3 + 8/81
Combining like terms, we get:
162/2 - 54/2 + 12/2 - 4/6 + 16/162
72 + 2/3
Therefore, the value of the expression 2*x^2 - 3x + 6 - 3/x +2/x^2 when x + 1/2 = 5 is 72 2/3.