2x^2-28/x^2-4

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Solution for 2x^2-28/x^2-4 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-(28/(x^2))-4 = 0

2*x^2-28*x^-2-4 = 0

t_1 = x^2

2*t_1^1-28*t_1^-1-4 = 0

2*t_1^1-28*t_1^-1-4*t_1^0 = 0

(2*t_1^2-4*t_1^1-28*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(2*t_1^2-4*t_1^1-28*t_1^0) = 0

t_1^1

2*t_1^2-4*t_1-28 = 0

2*t_1^2-4*t_1-28 = 0

DELTA = (-4)^2-(-28*2*4)

DELTA = 240

DELTA > 0

t_1 = (240^(1/2)+4)/(2*2) or t_1 = (4-240^(1/2))/(2*2)

t_1 = (4*15^(1/2)+4)/4 or t_1 = (4-4*15^(1/2))/4

t_1 in { (4-4*15^(1/2))/4, (4*15^(1/2)+4)/4} 

t_1 = (4-4*15^(1/2))/4

x^2-((4-4*15^(1/2))/4) = 0

1*x^2 = (4-4*15^(1/2))/4 // : 1

x^2 = (4-4*15^(1/2))/4

t_1 = (4*15^(1/2)+4)/4

x^2-((4*15^(1/2)+4)/4) = 0

1*x^2 = (4*15^(1/2)+4)/4 // : 1

x^2 = (4*15^(1/2)+4)/4

x^2 = (4*15^(1/2)+4)/4 // ^ 1/2

abs(x) = ((4*15^(1/2)+4)^(1/2))/2

x = ((4*15^(1/2)+4)^(1/2))/2 or x = -(((4*15^(1/2)+4)^(1/2))/2)

x in { ((4*15^(1/2)+4)^(1/2))/2, -(((4*15^(1/2)+4)^(1/2))/2) }

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