find three consecutive integers such that the product of the first and third is 35 greater than the product of the second and 5

Question

find three consecutive integers such that the product of the first and third is 35 greater than the product of the second and 5

Answer 1

1st integer is X

2nd integer is X+1

3rd integer is X+2

x(x+2) = 35 + 5(x+1)

x^2 + 2x = 35 + 5x + 5

x^2 + 2x = 5x + 40

x^2 -3x - 40 = 0

(x - 8)(x + 5) = 0

x=8 or x = -5

8,9,10 or -5,-4,-3