5-3/z=3/z^2

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Solution for 5-3/z=3/z^2 equation: 


D( z )

z^2 = 0

z = 0

z^2 = 0

z^2 = 0

1*z^2 = 0 // : 1

z^2 = 0

z = 0

z = 0

z = 0

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

5-(3/z) = 3/(z^2) // - 3/(z^2)

5-(3/z)-(3/(z^2)) = 0

5-3*z^-1-3*z^-2 = 0

t_1 = z^-1

5-3*t_1^2-3*t_1^1 = 0

5-3*t_1^2-3*t_1 = 0

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

DELTA = 69

DELTA > 0

t_1 = (69^(1/2)+3)/(-3*2) or t_1 = (3-69^(1/2))/(-3*2)

t_1 = (69^(1/2)+3)/(-6) or t_1 = (3-69^(1/2))/(-6)

t_1 = (69^(1/2)+3)/(-6)

z^-1-((69^(1/2)+3)/(-6)) = 0

1*z^-1 = (69^(1/2)+3)/(-6) // : 1

z^-1 = (69^(1/2)+3)/(-6)

-1 < 0

1/(z^1) = (69^(1/2)+3)/(-6) // * z^1

1 = ((69^(1/2)+3)/(-6))*z^1 // : (69^(1/2)+3)/(-6)

-6*(69^(1/2)+3)^-1 = z^1

z = -6*(69^(1/2)+3)^-1

t_1 = (3-69^(1/2))/(-6)

z^-1-((3-69^(1/2))/(-6)) = 0

1*z^-1 = (3-69^(1/2))/(-6) // : 1

z^-1 = (3-69^(1/2))/(-6)

-1 < 0

1/(z^1) = (3-69^(1/2))/(-6) // * z^1

1 = ((3-69^(1/2))/(-6))*z^1 // : (3-69^(1/2))/(-6)

-6*(3-69^(1/2))^-1 = z^1

z = -6*(3-69^(1/2))^-1

z in { -6*(69^(1/2)+3)^-1, -6*(3-69^(1/2))^-1 }

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