To solve this quadratic equation, let's first simplify it by letting x = Х+97.

So the equation becomes x² + 34x + 120 = 0.

Now, we can solve this quadratic equation by factoring or using the quadratic formula.

Factoring:
(x + 30)(x + 4) = 0
x = -30 or x = -4

However, since we let x = Х+97, we need to substitute back to find the value of Х:

Х+97 = -30
Х = -30 - 97
Х = -127

or

Х+97 = -4
Х = -4 - 97
Х = -101

Therefore, the solutions to the equation (Х+97)² + 34(Х+97) + 120 = 0 are Х = -127 or Х = -101.