The equation (x-1) / X - (8x + a) / 2x (x-1) + X / (x-1) = 0

The equation (x-1) / X - (8x + a) / 2x (x-1) + X / (x-1) = 0

(x-1)/x-(8x+a)/2x(x-1)+x/(x-1)=0
2(x-1)^2-(8x+a)+2x^2=0
2x^2-4x+2-8x-a+2x^2=0
4x^2-12x+2-a=0
△=144-16(2-a)=112+16a≥0
7+a≥0
a≥-7