First, let's distribute the (2-x) in the first part of the equation:

(2-x)(2+x) + 7.5x = 2 + x^2
(4 - 2x + 2x - x^2) + 7.5x = 2 + x^2

Now simplify:

4 - x^2 + 7.5x = 2 + x^2
7.5x - x^2 = -2 + x^2

Rearrange terms:

7.5x = -2 + 2x^2
2x^2 - 7.5x - 2 = 0

Now, we have a quadratic equation in the form of ax^2 + bx + c = 0. We can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Plugging in our values:

x = (7.5 ± sqrt((-7.5)^2 - 42(-2))) / 2*2
x = (7.5 ± sqrt(56.25 + 16))/4
x = (7.5 ± sqrt(72.25))/4
x = (7.5 ± 8.5)/4

So, the possible solutions are:

x = (7.5 + 8.5)/4 = 16/4 = 4
x = (7.5 - 8.5)/4 = -1/4 = -0.25

Therefore, the solutions to the equation are x = 4 and x = -0.25.