To solve this equation, we'll start by squaring both sides to remove the square root:

(x^2 - 2x - 4) = (2x^2 - 6x - 1)

Next, we'll combine like terms and move everything to one side of the equation:

0 = 2x^2 - x + 3

Now, let's factor the quadratic equation:

0 = (2x - 3)(x - 1)

Setting each factor to zero, we get two possible solutions:

2x - 3 = 0
x = 3/2

x - 1 = 0
x = 1

Therefore, the solutions to the equation sqrt(x^2-2x-4) = sqrt(2x^2-6x-1) are x = 3/2 and x = 1.