(6x-6/x+3)(x^2-3x-18/6x^2-6)

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Solution for (6x-6/x+3)(x^2-3x-18/6x^2-6) equation: 


D( x )

x = 0

x = 0

x = 0

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

(6*x-(6/x)+3)*(x^2-((18/6)*x^2)-(3*x)-6) = 0

(6*x-6*x^-1+3)*(x^2-3*x^2-3*x-6) = 0

(6*x-6*x^-1+3)*(-2*x^2-3*x-6) = 0

6*x-6*x^-1+3 = 0

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

2*x^1-2*x^-1+1*x^0 = 0

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

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

x^1

2*x^2+x-2 = 0

2*x^2+x-2 = 0

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

DELTA = 17

DELTA > 0

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

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

x in { (-(17^(1/2)+1))/4, (17^(1/2)-1)/4} 

3*(x+(17^(1/2)+1)/4)*(x-((17^(1/2)-1)/4)) = 0

-2*x^2-3*x-6 = 0

-1*(2*x^2+3*x+6) = 0

2*x^2+3*x+6 = 0

DELTA = 3^2-(2*4*6)

DELTA = -39

DELTA < 0

-1 = 0

-1*3*(x+(17^(1/2)+1)/4)*(x-((17^(1/2)-1)/4)) = 0

( x+(17^(1/2)+1)/4 )

x+(17^(1/2)+1)/4 = 0 // - (17^(1/2)+1)/4

x = -((17^(1/2)+1)/4)

( x-((17^(1/2)-1)/4) )

x-((17^(1/2)-1)/4) = 0 // + (17^(1/2)-1)/4

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

x in { -((17^(1/2)+1)/4), (17^(1/2)-1)/4 }

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