solve for x
(x^2 - x) + (x^2 - x)^1/2 -6 = 0
(sqrt(x^2-x)+3)(sqrt(x^2-x)-2)=0
two solutions
a) sqrt(x^2-x)=-3
b) sqrt(x^2-x)=2
square both sides...
a) x^2-x-9=0
b) x^2-x-4=0
which leads to
a) x=(1+-sqrt(1+36))/2
b) x=(1+-sqrt(1+16))/2
check my thinking, I hope I didn't error in the algebra.