Question 1008866
n, any positive integer, not 0;
The next integer is n+1.


{{{highlight_green(n(n+1)=n+(n+1)+19)}}}


{{{n^2+n=2n+20}}}
{{{n^2-n-20=0}}}
{{{(n+4)(n-5)=0}}}


n=-4 does not fit the problem's description.
n=5  is part of the solution.  The next or consecutive number after, is 6.