Question: Find two integers whose product is -18 and whose sum is 3.
Let the two integers be x and y. Then
x + y = 3 -- their sum is 3
xy = -18 -- their product is -18
From the 1st eqn, x = 3 - y. So substitute this into the 2nd equation. This gives
(3 - y)y = -18 -- multiply out
3y - y^2 = -18 -- arrange into a standard quadratic
y^2 - 3y - 18 = 0 -- now factorise
(y + 3)(y - 6) = 0
So, y = -3, or y = 6
And x = 3 - y
So, x = 6, or x = -3
In other words. the two integers are: -3 and 6