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x + y  = -1      →  y = -1 - x     (1)

x*y   = - 60    (2)

Put (1) into (2)

x (-1 - x)  = -60

-x - x^2  = -60   multiply through by -1  and rearrange

x^2 + x - 60   =   0     solving for x   we have

x =  [ - 1 + sqrt(241)] / 2    and y   =  [ - 1 - sqrt(241)] / 2        or

x = [ - 1 - sqrt(241)] / 2     and  y  =  [ - 1 + sqrt(241)] / 2

Technically, the two numbers are:

\(\frac{-1+\sqrt{241}}{2} \text{ . . .and. . . } \frac{-1-\sqrt{241}}{2}\)

I found just it by using the quadratic formula on this equation:

x² - x - 60 = 0

There are no integers that add to -1 but multiply to -60.

Does your problem look like this:

x² - x - 60 = 0

Or is there a number in front of the x²  ?