13-6x^2-6/(x^2)

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Solution for 13-6x^2-6/(x^2) equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

13-(6*x^2)-(6/(x^2)) = 0

13-6*x^2-6*x^-2 = 0

t_1 = x^2

13-6*t_1^1-6*t_1^-1 = 0

13*t_1^0-6*t_1^1-6*t_1^-1 = 0

(13*t_1^1-6*t_1^2-6*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(13*t_1^1-6*t_1^2-6*t_1^0) = 0

t_1^1

13*t_1-6*t_1^2-6 = 0

13*t_1-6*t_1^2-6 = 0

DELTA = 13^2-(-6*(-6)*4)

DELTA = 25

DELTA > 0

t_1 = (25^(1/2)-13)/(-6*2) or t_1 = (-25^(1/2)-13)/(-6*2)

t_1 = 2/3 or t_1 = 3/2

t_1 in { 2/3, 3/2} 

t_1 = 2/3

x^2-2/3 = 0

1*x^2 = 2/3 // : 1

x^2 = 2/3

x^2 = 2/3 // ^ 1/2

abs(x) = (2/3)^(1/2)

x = (2/3)^(1/2) or x = -(2/3)^(1/2)

t_1 = 3/2

x^2-3/2 = 0

1*x^2 = 3/2 // : 1

x^2 = 3/2

x^2 = 3/2 // ^ 1/2

abs(x) = (3/2)^(1/2)

x = (3/2)^(1/2) or x = -(3/2)^(1/2)

x in { (2/3)^(1/2), -(2/3)^(1/2), (3/2)^(1/2), -(3/2)^(1/2) }

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