Question

What numbers multiply to -30 and add to -3

Answer 1

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?