The crucial part of the wording of the problem tells us that the two integers are consecutive. So, let's call the first term x. Then the other term must be x + 1 since it comes right after it and is an integer. Now we can solve:
x(x + 1) = x + (x + 1) + 19
x^2 + x = 2x + 20
x^2 - x - 20 = 0
Now we factor:
(x - 5)(x + 4) = 0
This means x either equals 5 or x = -4 to satisfy the above equation. We know that x is positive from the question itself, so x must be 5. The number consecutively after it then must be 6.
