z-4/z-6=8/-5

Solution for z-4/z-6=8/-5 equation:

D( z )

z = 0

z = 0

z = 0

z in (-oo:0) U (0:+oo)

z-(4/z)-6 = 8/(-5) // - 8/(-5)

z-(4/z)-(8/(-5))-6 = 0

z-4*z^-1+8/5-6 = 0

1*z^1-4*z^-1-22/5*z^0 = 0

(1*z^2-22/5*z^1-4*z^0)/(z^1) = 0 // * z^2

z^1*(1*z^2-22/5*z^1-4*z^0) = 0

z^1

z^2+(-22/5)*z-4 = 0

z^2+(-22/5)*z-4 = 0

DELTA = (-22/5)^2-(-4*1*4)

DELTA = 884/25

DELTA > 0

z = ((884/25)^(1/2)-(-22/5))/(1*2) or z = (-(-22/5)-(884/25)^(1/2))/(1*2)

z = ((884/25)^(1/2)+22/5)/2 or z = (22/5-(884/25)^(1/2))/2

z in { (22/5-(884/25)^(1/2))/2, ((884/25)^(1/2)+22/5)/2} 

z in { (22/5-(884/25)^(1/2))/2, ((884/25)^(1/2)+22/5)/2 }