Let's solve each of these equations individually.

2² + 7 = 0
4 + 7 = 0
11 = 0 (This is incorrect, so there are no real solutions to this equation)

X² - 169 = 0
(X + 13)(X - 13) = 0
X + 13 = 0 or X - 13 = 0
X = -13 or X = 13

X² - 7x = 0
X(X - 7) = 0
X = 0 or X - 7 = 0
X = 0 or X = 7

-7x² - 46x + 21 = 0
Solve for x using the quadratic formula:
x = (-(-46) ± √((-46)² - 4(-7)21))/(2*(-7))
x = (46 ± √(2116 + 588))/(-14)
x = (46 ± √2704)/(-14)
x = (46 ± 52)/(-14)
x = (46 + 52)/(-14) or x = (46 - 52)/(-14)
x = 98/(-14) or x = -6/(-14)
x = -7 or x = 3/7

So the solutions to the equations provided are:

No real solutionsX = -13 or X = 13X = 0 or X = 7X = -7 or X = 3/7