1) The solutions to the equation x^2 - 2x + 10 = 0 can be found using the quadratic formula:

x = (-(-2) ± √((-2)^2 - 4110)) / 2*1
x = (2 ± √(4 - 40)) / 2
x = (2 ± √(-36)) / 2
x = (2 ± 6i) / 2

Thus, the solutions are x = 1 + 3i and x = 1 - 3i.

2) The solutions to the equation 3x^2 - 7x - 1 = 0 can also be found using the quadratic formula:

x = (7 ± √((-7)^2 - 43(-1))) / 2*3
x = (7 ± √(49 + 12)) / 6
x = (7 ± √61) / 6

Therefore, the solutions are x ≈ 2.52 and x ≈ -0.186.