4/5z+6/z-5

Solution for 4/5z+6/z-5 equation:

D( z )

z = 0

z = 0

z = 0

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

(4/5)*z+6/z-5 = 0

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

(4/5*z^2-5*z^1+6*z^0)/(z^1) = 0 // * z^2

z^1*(4/5*z^2-5*z^1+6*z^0) = 0

z^1

(4/5)*z^2-5*z+6 = 0

(4/5)*z^2-5*z+6 = 0

DELTA = (-5)^2-(4*6*(4/5))

DELTA = 29/5

DELTA > 0

z = ((29/5)^(1/2)+5)/(2*(4/5)) or z = (5-(29/5)^(1/2))/(2*(4/5))

z = 5/8*((29/5)^(1/2)+5) or z = 5/8*(5-(29/5)^(1/2))

z in { 5/8*(5-(29/5)^(1/2)), 5/8*((29/5)^(1/2)+5)} 

z in { 5/8*(5-(29/5)^(1/2)), 5/8*((29/5)^(1/2)+5) }