To solve the equation 4x^2 + 2 + 5x^4 - 3 = 137, we can start by simplifying the equation:

4x^2 + 5x^4 - 1 = 137

Next, we can move all the terms to one side of the equation to set it equal to zero:

5x^4 + 4x^2 - 138 = 0

Now, we can try to factor the equation. However, this equation does not seem to be easily factorable. Therefore, we can use numerical methods to approximate the solutions.

Using a graphing calculator or a computer program, we can find that the approximate solutions to this equation are x ≈ -2.5, x ≈ -1.4, x ≈ 1.4, and x ≈ 2.5.