Product of two consecutive integers is:
n(n+1)=n²+n
Sum of two consecutive integers is:
n+(n+1)=n+n+1=2n+1
What you have proclaimed:
n²+n=2n+1+29
n²+n=2n+30
n²+n-2n-30=0
n²-n-30=0
(n-6)(n+5)=0
Therefore n=6 or n=-5.
When n=6,
n+1=7
First answer: 6 and 7.
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When n=-5,
n+1=-4
Second answer: -4 and -5.