Question

What two consecutive numbers have a product of 22952

Answer 1

$x(x+1)=22952\\ \\ x^2+x-22952=0\\ \\ \Delta=1^2-4.1.(-22952)=1+91808=91809\\ \\ x=\frac{-1+\sqrt{91809}}{2}=\frac{-1+303}{2}=\frac{302}{2}=151$

Numbers are: 151 and 152

Answer 2

$n(n+1)=22952\\ n^2+n-22952=0\\ \Delta=1^2-4\cdot1\cdot(-22952)=91809\\ \sqrt{\Delta}=\sqrt{91809}=303\\ n_1=\frac{-1-303}{2\cdot1}=\frac{-304}{2}=-152\\ n_2=\frac{-1+303}{2\cdot1}=\frac{302}{2}=151\\\\ n_1+1=-152+1=-151\\ n_2+1=151+1=152$

Those numbers are -152 and -151 or 151 and 152.