The product of two consecutive positive integers is 6 more than six times the sum of the two integers. Find the two integers.

Answer 1

x(x+1) = 6+6(x+x+1)

x^2 + x = 12x + 12

x^2 -11x - 12 = 0

(x-12)(x+1) = 0

x = 12

x+1 = 13

the two integers are 12 and 13

12(13 = 156

6+6(12+13) 156