What multiplies to negative 24 and adds to 2

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

Then

xy = - 24

x = - (24/y)

And

x + y = 2

Putting the value of x from the first equation in the second equation, we get

x + y = 2

- (24/y) + y = 2

- 24 + y^2 = 2y

y^2 - 2y - 24 = 0

y^2 - 6y + 4y - 24 = 0

y (y - 6) + 4 (y - 6) = 0

(y - 6) (y + 4) = 0

When

y - 6 = 0

y = 6

Then

x + y = 2

x + 6 = 2

x = 2 - 6

= - 4

And when

y + 4 = 0

y = - 4

Then

x + y = 2

x - 4 = 2

x = 2 + 4

= 6

So the two unknown numbers are - 4 and 6.