To solve the equation √x-2 -3√x^2-4=0, we can simplify it step by step:

1. Let's simplify the expression √x-2:
√x-2 = √(x-2)

2. Now let's simplify the expression 3√x^2-4:
3√x^2-4 = 3√(x^2-4)

3. Substitute these simplified expressions back into the original equation:
√(x-2) - 3√(x^2-4) = 0

4. To eliminate the square roots, we can square both sides of the equation:
(√(x-2))^2 - (3√(x^2-4))^2 = 0^2
(x-2) - 9(x^2-4) = 0

5. Expand and simplify the equation:
x - 2 - 9x^2 + 36 = 0
-9x^2 + x + 34 = 0

6. Rearrange the equation in standard quadratic form:
-9x^2 + x + 34 = 0
9x^2 - x - 34 = 0

7. Solve the quadratic equation using factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 9, b = -1, and c = -34:
x = (-(-1) ± √((-1)^2 - 4(9)(-34))) / (2(9))
x = (1 ± √(1 + 1224)) / 18
x = (1 ± √1225) / 18
x = (1 ± 35) / 18

8. Solve for x:
x = (1 + 35) / 18 = 36 / 18 = 2
x = (1 - 35) / 18 = -34 / 18 = -17/9

Therefore, the solutions to the equation √x-2 -3√x^2-4=0 are x = 2 and x = -17/9.