Let's solve the equation step by step:

1/2x^2 + 11.5 + 2x^2 = 2x^2 - 10

Combine like terms:

(1/2 + 2)x^2 + 11.5 = 2x^2 - 10

(5/2)x^2 + 11.5 = 2x^2 - 10

Now, subtract 2x^2 from both sides:

(5/2)x^2 - 2x^2 + 11.5 = -10

(5/2 - 2)x^2 + 11.5 = -10

(5/2 - 4/2)x^2 + 11.5 = -10

(1/2)x^2 + 11.5 = -10

Subtract 11.5 from both sides:

(1/2)x^2 = -10 - 11.5

(1/2)x^2 = -21.5

Now, multiply by 2 to get rid of the fraction:

x^2 = -43

Take the square root of both sides:

x = ±√(-43)

As the square root of a negative number is not a real number, the solution to the equation is not possible in the real number system.