z=54/z-3

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Solution for z=54/z-3 equation: 


D( z )

z = 0

z = 0

z = 0

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

z = 54/z-3 // - 54/z-3

z-(54/z)+3 = 0

z-54*z^-1+3 = 0

1*z^1-54*z^-1+3*z^0 = 0

(1*z^2+3*z^1-54*z^0)/(z^1) = 0 // * z^2

z^1*(1*z^2+3*z^1-54*z^0) = 0

z^1

z^2+3*z-54 = 0

z^2+3*z-54 = 0

DELTA = 3^2-(-54*1*4)

DELTA = 225

DELTA > 0

z = (225^(1/2)-3)/(1*2) or z = (-225^(1/2)-3)/(1*2)

z = 6 or z = -9

z in { -9, 6} 

z in { -9, 6 }

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