1/z=3z-4/5

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Solution for 1/z=3z-4/5 equation: 


D( z )

z = 0

z = 0

z = 0

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

1/z = 3*z-(4/5) // - 3*z-(4/5)

1/z-(3*z)+4/5 = 0

1/z-3*z+4/5 = 0

1*z^-1-3*z^1+4/5*z^0 = 0

(4/5*z^1-3*z^2+1*z^0)/(z^1) = 0 // * z^2

z^1*(4/5*z^1-3*z^2+1*z^0) = 0

z^1

(4/5)*z-3*z^2+1 = 0

(4/5)*z-3*z^2+1 = 0

DELTA = (4/5)^2-(-3*1*4)

DELTA = 316/25

DELTA > 0

z = ((316/25)^(1/2)-(4/5))/(-3*2) or z = (-(4/5)-(316/25)^(1/2))/(-3*2)

z = ((316/25)^(1/2)-4/5)/(-6) or z = ((316/25)^(1/2)+4/5)/6

z in { ((316/25)^(1/2)-4/5)/(-6), ((316/25)^(1/2)+4/5)/6} 

z in { ((316/25)^(1/2)-4/5)/(-6), ((316/25)^(1/2)+4/5)/6 }

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