What numbers multiply to - 30 and add to - 3

Let the numbers be x and y. Then xy = - 30 and x+y = - 3.

Solve xy = - 30 for y: y = - 30/x

subst. - 30/x for y in x+y = - 3: x - 30/x = - 3

Multiply all 3 terms by x: x^2 - 30 = - 3x, so x^2 + 3x - 10 = 0

Solve this quadratic equation for x. x: {-5, 2}

If x = - 5, then x+y = - 3 becomes - 5 + y = - 3, and y = 2.

You should check to determine whether x=2 is also correct. If it is, what is the corresponding y value?