To solve the equation 2x^2 = 9/2, we can start by multiplying both sides of the equation by 2 to eliminate the fraction:

2 * 2x^2 = 2 * (9/2)

This simplifies to:

4x^2 = 9

Next, we can divide both sides of the equation by 4 to isolate x^2:

4x^2 / 4 = 9 / 4

This simplifies to:

x^2 = 9/4

To solve for x, we can take the square root of both sides of the equation:

√(x^2) = √(9/4)

This simplifies to:

x = ± √(9/4)

The square root of 9 is 3, and the square root of 4 is 2, so we have:

x = ± (3/2)

Therefore, the solutions to the equation 2x^2 = 9/2 are x = 3/2 and x = -3/2.