What two number mutiply to - 240 but add up to 8

Let us assume the two unknown numbers to be "x" and "y".

Then

xy = - 240

x = - (240/y)

And

x + y = 8

Now let us put the value of x in the second equation. We get

x + y = 8

- (240/y) + y = 8

y^2 - 240 = 8y

y^2 - 8y - 240 = 0

y^2 - 20y + 12y - 240 = 0

y (y - 20) + 12 (y - 20) = 0

(y - 20) (y + 12) = 0

So we can see that the unknown number y can have two values and hence the unknown number will also have two values.

When

y - 20 = 0

y = 20

Then

xy = - 240

20x = - 240

x = - 12

So we can see that when y is equal to 20 then x is equal to - 12 and when y is equal to - 12 then x is equal to 20. So the two numbers are 20 and - 12.