Three positive consecutive integers are n, n+1, and n+2. And these integers satisfy:
n(n+1)=9(n+2)+2 expanding each side gives you:
n^2+n=9n+18+2
n^2+n=9n+20 subtract 9n from both sides
n^2-8n=20 subtract 20 from both sides
n^2-8n-20=0 now factor
n^2+2n-10n-20=0
n(n+2)-10(n+2)=0
(n-10)(n+2)=0, since we only want positive integers
n=10
So the three integers are 10, 11, 12
