(1/n) + [1(n+1)] = -43/462
(2n + 1)/(n2 + n) = -43/462
Cross multiply, expand and collect to get: 43n2 + 967n + 462 = 0
The quadratic formula gives n = -22 and an extraneous root
The 2 integers are, therefore, -22 and -21
You should plug these numbers back into the original problem to be sure they work!