[tex] \frac{(n+2)!}{n!} = 72\\\\
\frac{n!(n+1)(n+2)}{n!} = 72\\\\
(n+1)(n+2) = 72\\
n^2 + 3n + 2 - 72 = 0\\
n^2 + 3n - 70 = 0\\
\Delta = 9 - 4*(-70) = 9 + 289\\\\
x_{1, 2} = \frac{-3 \pm \sqrt{289} }{2} = \frac{-3 \pm 13}{2} => \left \{ {{x_{1}=5} \atop {x_{2}=-8}} \right. \\\\
\mbox{n! exista pentru orice n} \in N => x = 5[/tex]
