What adds to -3 and multiplies to -36

Take the two conditions that you've given us:

 . . . x + y = -3

 . . . xy = -36

Massage the first equation to say [ y = -x - 3 ], then substitute that one into
the second equation, and the second equation becomes

                     x² + 3x - 36 = 0 .

That one can't be easily factored, but you can mash it through
the quadratic formula, and discover that . . .

x =  -1.5  (plus and minus)  1/2 √153

so the two numbers are

         - 7.68466 (rounded)
and
        + 4.68466 (rounded).

Check:

     4.68466 7.68466  =  -3

     (4.68466) x (-7.68466)  = -36.00002 (rounded)                         yay !
      

Xis -1/2
y is 35/4.