To solve the inequality 3x^2 - |x-3| > 9x - 2, we will consider two cases:

Case 1: x ≥ 3
In this case, the absolute value part |x-3| becomes x-3 since x is greater than or equal to 3.
So, the inequality becomes 3x^2 - (x-3) > 9x - 2
Expanding and simplifying, we get:
3x^2 - x + 3 > 9x - 2
3x^2 - 10x + 5 > 0
Solving this quadratic inequality we get:
x < 0.33 or x > 5.00

Case 2: x < 3
In this case, the absolute value part |x-3| becomes -(x-3) since x is less than 3.
So, the inequality becomes 3x^2 - -(x-3) > 9x - 2
Expanding and simplifying, we get:
3x^2 + x - 3 > 9x - 2
3x^2 - 8x + 1 > 0
Solving this quadratic inequality we get:
x < 0.17 or x > 2.83

Combining these results, the solution to the inequality 3x^2 - |x-3| > 9x - 2 is:
x < 0.17 or x > 5.00

For the equation x^2 - 6|x| - 2=0, let y = |x|, the equation becomes y^2 - 6y - 2 = 0
Solving this quadratic equation we get:
y = 3 ± √11

Since y = |x|, x can be positive or negative when y = 3 + √11 or y = 3 - √11 respectively.

Therefore, the solutions for x are:
x = √(11) or x = -√(11)