(4x-1/x)=-1

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Solution for (4x-1/x)=-1 equation: 


D( x )

x = 0

x = 0

x = 0

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

4*x-(1/x) = -1 // + 1

4*x-(1/x)+1 = 0

4*x-x^-1+1 = 0

4*x^1-1*x^-1+1*x^0 = 0

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

x^1*(4*x^2+1*x^1-1*x^0) = 0

x^1

4*x^2+x-1 = 0

4*x^2+x-1 = 0

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

DELTA = 17

DELTA > 0

x = (17^(1/2)-1)/(2*4) or x = (-17^(1/2)-1)/(2*4)

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

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

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

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