If you have one solution you can find the other by just looking at
x^2+x-a=0 where a:=y^2-y .
We already know x^2+x-a=0 has one real solution (x1=y-1). Factoring this polynomial gives x^2+x-a=(x-x1)*(x-x2) and comparing the coefficient of x we get 1=-x1-x2 or x2=-1-x1=-1-y+1=-y. This is how you could get x2.

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