1) -2 +d-3d² < 0

Rearrange the terms to make the quadratic equation more visible:
-3d² + d - 2 < 0

Now, we can solve this quadratic inequality by finding the roots of the equation -3d² + d - 2 = 0.

Solving the equation, we get:

d = (-1 ± √(1 - 4(-3)(-2))) / 2*(-3)
d = (-1 ± √(1 - 24)) / -6
d = (-1 ± √(-23)) / -6
d = (-1 ± i√23) / -6

Since the quadratic equation has complex solutions, we can find the critical points by setting -3d² + d - 2 equal to zero:

-3d² + d - 2 = 0
d = (-1 ± √(1 - 4(-3)(-2))) / 2*(-3)
d = (-1 ± √(1 - 24)) / -6
d = (-1 ± √(-23)) / -6
d = (-1 ± i√23) / -6

Therefore, the solution to the quadratic inequality -2 +d-3d² < 0 is:
(-1 - i√23) / -6 < d < (-1 + i√23) / -6

2) 2a²-2x-7 > x²+5x-17

Rearrange the terms to make the quadratic equation more visible:
2a² - 2x - 7 > x² + 5x - 17

Subtract x² + 5x - 17 from both sides to get the inequality in standard form:
2a² - 7 > x² + 5x - 2x - 17
2a² - 7 > x² + 3x - 17

Now, to solve this quadratic inequality, we can set it equal to zero and solve for x:
2a² - 7 = x² + 3x - 17
x² + 3x - 17 - (2a² - 7) = 0
x² + 3x - 17 - 2a² + 7 = 0
x² + 3x - 2a² - 10 = 0

Using the quadratic formula, we can solve for x in terms of a:
x = (-3 ± √(9 + 4*(2a² + 10))) / 2

Therefore, the solution to the inequality 2a² - 2x - 7 > x² + 5x - 17 is:
x < (-3 - √(9 + 8a² + 40)) / 2 or x > (-3 + √(9 + 8a² + 40)) / 2