WELL YOU SHOLD KNOW

Did you try to take its square root? Try it and take the two integers closest to it.

Hint: one just above and the other just below.

$x(x+1)=272 \\ x^2 + x =272 \\ (x+1/2)^2 -\dfrac 1 4 = 272 \\ (x+1/2)^2 = \dfrac {1089}{4} \\ x+\dfrac 1 2 = \sqrt{\dfrac {1089}{4}} = \dfrac {33}{2} \\ x=\dfrac {32}{2} = 16 \\ \mbox{the two numbers are }16 \mbox{ and } 17$

$-16 \mbox{ and } -17 \mbox{ work as well.}$