9/2z-1=3/z

Solution for 9/2z-1=3/z equation:

D( z )

z = 0

z = 0

z = 0

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

(9/2)*z-1 = 3/z // - 3/z

(9/2)*z-(3/z)-1 = 0

(9/2)*z-3*z^-1-1 = 0

9/2*z^1-3*z^-1-1*z^0 = 0

(9/2*z^2-1*z^1-3*z^0)/(z^1) = 0 // * z^2

z^1*(9/2*z^2-1*z^1-3*z^0) = 0

z^1

(9/2)*z^2-z-3 = 0

(9/2)*z^2-z-3 = 0

DELTA = (-1)^2-(-3*4*(9/2))

DELTA = 55

DELTA > 0

z = (55^(1/2)+1)/(2*(9/2)) or z = (1-55^(1/2))/(2*(9/2))

z = (55^(1/2)+1)/9 or z = (1-55^(1/2))/9

z in { (1-55^(1/2))/9, (55^(1/2)+1)/9} 

z in { (1-55^(1/2))/9, (55^(1/2)+1)/9 }