w-1/w=8

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Solution for w-1/w=8 equation: 


D( w )

w = 0

w = 0

w = 0

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

w-(1/w) = 8 // - 8

w-(1/w)-8 = 0

w-w^-1-8 = 0

1*w^1-1*w^-1-8*w^0 = 0

(1*w^2-8*w^1-1*w^0)/(w^1) = 0 // * w^2

w^1*(1*w^2-8*w^1-1*w^0) = 0

w^1

w^2-8*w-1 = 0

w^2-8*w-1 = 0

DELTA = (-8)^2-(-1*1*4)

DELTA = 68

DELTA > 0

w = (68^(1/2)+8)/(1*2) or w = (8-68^(1/2))/(1*2)

w = (2*17^(1/2)+8)/2 or w = (8-2*17^(1/2))/2

w in { (8-2*17^(1/2))/2, (2*17^(1/2)+8)/2} 

w in { (8-2*17^(1/2))/2, (2*17^(1/2)+8)/2 }

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