z-3/2+3=z^2-9/z^2+z-12

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Solution for z-3/2+3=z^2-9/z^2+z-12 equation: 


D( z )

z^2 = 0

z^2 = 0

z^2 = 0

1*z^2 = 0 // : 1

z^2 = 0

z = 0

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

z-(3/2)+3 = z^2+z-(9/(z^2))-12 // - z^2+z-(9/(z^2))-12

z-z^2-z+9/(z^2)-(3/2)+3+12 = 0

z-z^2-z+9/(z^2)-3/2+3+12 = 0

9*z^-2-z^2+27/2 = 0

t_1 = z^2

9*t_1^-1-1*t_1^1+27/2 = 0

9*t_1^-1-1*t_1^1+27/2*t_1^0 = 0

(27/2*t_1^1-1*t_1^2+9*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(27/2*t_1^1-1*t_1^2+9*t_1^0) = 0

t_1^1

(27/2)*t_1-t_1^2+9 = 0

(27/2)*t_1-t_1^2+9 = 0

DELTA = (27/2)^2-(-1*4*9)

DELTA = 873/4

DELTA > 0

t_1 = ((873/4)^(1/2)-(27/2))/(-1*2) or t_1 = (-(27/2)-(873/4)^(1/2))/(-1*2)

t_1 = ((873/4)^(1/2)-27/2)/(-2) or t_1 = ((873/4)^(1/2)+27/2)/2

t_1 in { ((873/4)^(1/2)-27/2)/(-2), ((873/4)^(1/2)+27/2)/2} 

t_1 = ((873/4)^(1/2)-27/2)/(-2)

z^2-(((873/4)^(1/2)-27/2)/(-2)) = 0

1*z^2 = ((873/4)^(1/2)-27/2)/(-2) // : 1

z^2 = ((873/4)^(1/2)-27/2)/(-2)

t_1 = ((873/4)^(1/2)+27/2)/2

z^2-(((873/4)^(1/2)+27/2)/2) = 0

1*z^2 = ((873/4)^(1/2)+27/2)/2 // : 1

z^2 = ((873/4)^(1/2)+27/2)/2

z^2 = ((873/4)^(1/2)+27/2)/2 // ^ 1/2

abs(z) = (((873/4)^(1/2)+27/2)^(1/2))/(2^(1/2))

z = (((873/4)^(1/2)+27/2)^(1/2))/(2^(1/2)) or z = -((((873/4)^(1/2)+27/2)^(1/2))/(2^(1/2)))

z in { (((873/4)^(1/2)+27/2)^(1/2))/(2^(1/2)), -((((873/4)^(1/2)+27/2)^(1/2))/(2^(1/2))) }

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