don't you know your quadratic formula...

y = x(x+1) = x^2 + x
x^2 + x - y = 0
x = [-1 p/m (1^2 +4y)^(1/2) ] / 2

where p/m means plus or minus.

thus:
x = [-1 + (1+4y)^(1/2) ] / 2
or
x = [-1 - (1+4y)^(1/2) ] /2

where (1+4y)^(1/2) is solvable using real numbers only if y >= -0.25.