Turn this into an equation: k2+k=60, so that we can find the zeroes or roots.
k2+k+¼=60+¼,
(k+½)2=60.25,
k+½=±√60.25=±7.7621 approx,
k=-½±7.7621=7.2621 or -8.2621.
If your question had been k(k+1)-600, the answer would have been:
k2+k-600=(k+25)(k-24), so k=-25 or 24. (I think this might have been the expected answer so the question wasn't quite right.)