2x^2+15/x^2=12

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Solution for 2x^2+15/x^2=12 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)

2*x^2+15/(x^2) = 12 // - 12

2*x^2+15/(x^2)-12 = 0

2*x^2+15*x^-2-12 = 0

t_1 = x^2

2*t_1^1+15*t_1^-1-12 = 0

2*t_1^1+15*t_1^-1-12*t_1^0 = 0

(2*t_1^2-12*t_1^1+15*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(2*t_1^2-12*t_1^1+15*t_1^0) = 0

t_1^1

2*t_1^2-12*t_1+15 = 0

2*t_1^2-12*t_1+15 = 0

DELTA = (-12)^2-(2*4*15)

DELTA = 24

DELTA > 0

t_1 = (24^(1/2)+12)/(2*2) or t_1 = (12-24^(1/2))/(2*2)

t_1 = (2*6^(1/2)+12)/4 or t_1 = (12-2*6^(1/2))/4

t_1 in { (12-2*6^(1/2))/4, (2*6^(1/2)+12)/4} 

t_1 = (12-2*6^(1/2))/4

x^2-((12-2*6^(1/2))/4) = 0

1*x^2 = (12-2*6^(1/2))/4 // : 1

x^2 = (12-2*6^(1/2))/4

x^2 = (12-2*6^(1/2))/4 // ^ 1/2

abs(x) = ((12-2*6^(1/2))^(1/2))/2

x = ((12-2*6^(1/2))^(1/2))/2 or x = -(((12-2*6^(1/2))^(1/2))/2)

t_1 = (2*6^(1/2)+12)/4

x^2-((2*6^(1/2)+12)/4) = 0

1*x^2 = (2*6^(1/2)+12)/4 // : 1

x^2 = (2*6^(1/2)+12)/4

x^2 = (2*6^(1/2)+12)/4 // ^ 1/2

abs(x) = ((2*6^(1/2)+12)^(1/2))/2

x = ((2*6^(1/2)+12)^(1/2))/2 or x = -(((2*6^(1/2)+12)^(1/2))/2)

x in { ((12-2*6^(1/2))^(1/2))/2, -(((12-2*6^(1/2))^(1/2))/2), ((2*6^(1/2)+12)^(1/2))/2, -(((2*6^(1/2)+12)^(1/2))/2) }

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