To solve the equation, we need to first simplify it:

(x-2)(x-1)x - x^2 - x/2 = 4.5x
(x^2 - 3x + 2)*x - x^2 - x/2 = 4.5x
x^3 - 3x^2 + 2x - x^2 - x/2 = 4.5x
x^3 - 4x^2 + 2x - x/2 = 4.5x

Now, let's combine like terms:

x^3 - 4x^2 + 2x - x/2 - 4.5x = 0
x^3 - 4x^2 - 1.5x = 0

Now, let's solve for x. There are a few ways to do this; one way is by factoring out an x:

x(x^2 - 4x - 1.5) = 0

Now, we can set each factor equal to zero:

x = 0

To find the other solutions, we can use the quadratic formula:

x = [4 ± sqrt(16 + 6)] / 2
x = [4 ± sqrt(22)] / 2
x = (4 ± √22) / 2

Therefore, the solutions to the equation are:

x = 0, (4 + √22) / 2, (4 - √22) / 2