1/z=12/10z-8

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Solution for 1/z=12/10z-8 equation: 


D( z )

z = 0

z = 0

z = 0

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

1/z = (12/10)*z-8 // - (12/10)*z-8

1/z-((12/10)*z)+8 = 0

(-6/5)*z+1/z+8 = 0

1*z^-1-6/5*z^1+8*z^0 = 0

(8*z^1-6/5*z^2+1*z^0)/(z^1) = 0 // * z^2

z^1*(8*z^1-6/5*z^2+1*z^0) = 0

z^1

(-6/5)*z^2+8*z+1 = 0

(-6/5)*z^2+8*z+1 = 0

DELTA = 8^2-(1*4*(-6/5))

DELTA = 344/5

DELTA > 0

z = ((344/5)^(1/2)-8)/(2*(-6/5)) or z = (-(344/5)^(1/2)-8)/(2*(-6/5))

z = -5/12*((344/5)^(1/2)-8) or z = 5/12*((344/5)^(1/2)+8)

z in { -5/12*((344/5)^(1/2)-8), 5/12*((344/5)^(1/2)+8)} 

z in { -5/12*((344/5)^(1/2)-8), 5/12*((344/5)^(1/2)+8) }

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