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?