z-4/z-8=5/7

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Solution for z-4/z-8=5/7 equation:


D( z )

z = 0

z = 0

z = 0

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

z-(4/z)-8 = 5/7 // - 5/7

z-(4/z)-(5/7)-8 = 0

z-4*z^-1-5/7-8 = 0

1*z^1-4*z^-1-61/7*z^0 = 0

(1*z^2-61/7*z^1-4*z^0)/(z^1) = 0 // * z^2

z^1*(1*z^2-61/7*z^1-4*z^0) = 0

z^1

z^2+(-61/7)*z-4 = 0

z^2+(-61/7)*z-4 = 0

DELTA = (-61/7)^2-(-4*1*4)

DELTA = 4505/49

DELTA > 0

z = ((4505/49)^(1/2)-(-61/7))/(1*2) or z = (-(-61/7)-(4505/49)^(1/2))/(1*2)

z = ((4505/49)^(1/2)+61/7)/2 or z = (61/7-(4505/49)^(1/2))/2

z in { (61/7-(4505/49)^(1/2))/2, ((4505/49)^(1/2)+61/7)/2}

z in { (61/7-(4505/49)^(1/2))/2, ((4505/49)^(1/2)+61/7)/2 }

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