Let the integers be x and x+1

Given that sum of consecutive positive integers is 613.Now,Acc. to statement:

=>x^2+(x+1)^2=613

=> x^2+x2+1+2x=613

=> 2x^2+2x=612

=> x^2 + (x + 1)^2 = 613

=> x^2 + x^2 + 1 + 2x = 612

=> 2x^2 + 2x = 612

=> 2x^2 + 2x - 612 = 0

=> 2(x^2 + x - 306) = 0

=> x^2 + 18x - 17x - 306 = 0