z+5/z+6=8/-5

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Solution for z+5/z+6=8/-5 equation: 


D( z )

z = 0

z = 0

z = 0

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

z+5/z+6 = 8/(-5) // - 8/(-5)

z+5/z-(8/(-5))+6 = 0

z+5/z+8/5+6 = 0

1*z^1+5*z^-1+38/5*z^0 = 0

(1*z^2+38/5*z^1+5*z^0)/(z^1) = 0 // * z^2

z^1*(1*z^2+38/5*z^1+5*z^0) = 0

z^1

z^2+(38/5)*z+5 = 0

z^2+(38/5)*z+5 = 0

DELTA = (38/5)^2-(1*4*5)

DELTA = 944/25

DELTA > 0

z = ((944/25)^(1/2)-(38/5))/(1*2) or z = (-(38/5)-(944/25)^(1/2))/(1*2)

z = ((944/25)^(1/2)-38/5)/2 or z = (-((944/25)^(1/2)+38/5))/2

z in { (-((944/25)^(1/2)+38/5))/2, ((944/25)^(1/2)-38/5)/2} 

z in { (-((944/25)^(1/2)+38/5))/2, ((944/25)^(1/2)-38/5)/2 }

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