x/1-1/x=8/3

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Solution for x/1-1/x=8/3 equation: 


D( x )

x = 0

x = 0

x = 0

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

x/1-(1/x) = 8/3 // - 8/3

x/1-(1/x)-(8/3) = 0

x-x^-1-8/3 = 0

1*x^1-1*x^-1-8/3*x^0 = 0

(1*x^2-8/3*x^1-1*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-8/3*x^1-1*x^0) = 0

x^1

x^2+(-8/3)*x-1 = 0

x^2+(-8/3)*x-1 = 0

DELTA = (-8/3)^2-(-1*1*4)

DELTA = 100/9

DELTA > 0

x = ((100/9)^(1/2)-(-8/3))/(1*2) or x = (-(-8/3)-(100/9)^(1/2))/(1*2)

x = 3 or x = -1/3

x in { -1/3, 3} 

x in { -1/3, 3 }

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