One integer is 5 less than another and their product is 84. Find the integers.

The first integer is going to be x and the second one is going to be y.

We now turn the clues into equations:

x = y - 5

xy = 84

The substitution method:

(y - 5) y = 84

y^2 - 5y - 84 = 0

(y+7) (y-12) = 0

y = - 7, 12.

If y = - 7, then x = - 12.

If y = 12, then x = 7