4(x^2-4)/x-2

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Solution for 4(x^2-4)/x-2 equation: 


D( x )

x = 0

x = 0

x = 0

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

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

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

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

4*x^2-2*x-16 = 0

4*x^2-2*x-16 = 0

2*(2*x^2-x-8) = 0

2*x^2-x-8 = 0

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

DELTA = 65

DELTA > 0

x = (65^(1/2)+1)/(2*2) or x = (1-65^(1/2))/(2*2)

x = (65^(1/2)+1)/4 or x = (1-65^(1/2))/4

2*(x-((1-65^(1/2))/4))*(x-((65^(1/2)+1)/4)) = 0

(2*(x-((1-65^(1/2))/4))*(x-((65^(1/2)+1)/4)))/x = 0

(2*(x-((1-65^(1/2))/4))*(x-((65^(1/2)+1)/4)))/x = 0 // * x

2*(x-((1-65^(1/2))/4))*(x-((65^(1/2)+1)/4)) = 0

( x-((1-65^(1/2))/4) )

x-((1-65^(1/2))/4) = 0 // + (1-65^(1/2))/4

x = (1-65^(1/2))/4

( x-((65^(1/2)+1)/4) )

x-((65^(1/2)+1)/4) = 0 // + (65^(1/2)+1)/4

x = (65^(1/2)+1)/4

x in { (1-65^(1/2))/4, (65^(1/2)+1)/4 }

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