find 3 positive consecutive integers such that the product of the first and the third integer is 17 more than three times the second integer
x ( x + 2) = 3(x + 1) + 17 simplify
x^2 + 2x = 3x + 20 rearrange as
x^2 - x -20 = 0 factor as
(x -5) ( x + 4) =20
The first factor is what we need
x - 5 = 0
x = 5
x + 1 = 6
x + 2 = 7
Proof
5*7 = 3 (6) + 17
35 = 18 + 17 (true)
