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

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

2*x^3-8*x^2-4*x = 0

2*x^3-8*x^2-4*x = 0

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

x^2-4*x-2 = 0

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

DELTA = 24

DELTA > 0

x = (24^(1/2)+4)/(1*2) or x = (4-24^(1/2))/(1*2)

x = (2*6^(1/2)+4)/2 or x = (4-2*6^(1/2))/2

2*x*(x-((4-2*6^(1/2))/2))*(x-((2*6^(1/2)+4)/2)) = 0

(2*x*(x-((4-2*6^(1/2))/2))*(x-((2*6^(1/2)+4)/2)))/x = 0

(2*x*(x-((4-2*6^(1/2))/2))*(x-((2*6^(1/2)+4)/2)))/x = 0 // * x

2*x*(x-((4-2*6^(1/2))/2))*(x-((2*6^(1/2)+4)/2)) = 0

( 2*x )

2*x = 0 // : 2

x = 0

( x-((2*6^(1/2)+4)/2) )

x-((2*6^(1/2)+4)/2) = 0 // + (2*6^(1/2)+4)/2

x = (2*6^(1/2)+4)/2

( x-((4-2*6^(1/2))/2) )

x-((4-2*6^(1/2))/2) = 0 // + (4-2*6^(1/2))/2

x = (4-2*6^(1/2))/2

x in { 0}

x in { (2*6^(1/2)+4)/2, (4-2*6^(1/2))/2 }

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