If we arrange the seats in r rows with s seats in each row, we have
[tex]rs=952[/tex]
Since the number of rows is 6 less than the number of seats in each row, we have
[tex]r=s-6[/tex]
Substitute this in the first equation to get
[tex](s-6)s=952 \iff s^2-6s-952=0[/tex]
This equation has solutions -28 and 34. We can't accept negative solutions (we would have -28 seats in each row...what would that mean??), the only feasible solution is 34.
So, we have
[tex]r=s-6=34-6=28[/tex]
rows with 34 seats per row.
