4x^2-20/x^2-25

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Solution for 4x^2-20/x^2-25 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)

4*x^2-(20/(x^2))-25 = 0

4*x^2-20*x^-2-25 = 0

t_1 = x^2

4*t_1^1-20*t_1^-1-25 = 0

4*t_1^1-20*t_1^-1-25*t_1^0 = 0

(4*t_1^2-25*t_1^1-20*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(4*t_1^2-25*t_1^1-20*t_1^0) = 0

t_1^1

4*t_1^2-25*t_1-20 = 0

4*t_1^2-25*t_1-20 = 0

DELTA = (-25)^2-(-20*4*4)

DELTA = 945

DELTA > 0

t_1 = (945^(1/2)+25)/(2*4) or t_1 = (25-945^(1/2))/(2*4)

t_1 = (3*105^(1/2)+25)/8 or t_1 = (25-3*105^(1/2))/8

t_1 in { (25-3*105^(1/2))/8, (3*105^(1/2)+25)/8} 

t_1 = (25-3*105^(1/2))/8

x^2-((25-3*105^(1/2))/8) = 0

1*x^2 = (25-3*105^(1/2))/8 // : 1

x^2 = (25-3*105^(1/2))/8

t_1 = (3*105^(1/2)+25)/8

x^2-((3*105^(1/2)+25)/8) = 0

1*x^2 = (3*105^(1/2)+25)/8 // : 1

x^2 = (3*105^(1/2)+25)/8

x^2 = (3*105^(1/2)+25)/8 // ^ 1/2

abs(x) = ((3*105^(1/2)+25)^(1/2))/(2*2^(1/2))

x = ((3*105^(1/2)+25)^(1/2))/(2*2^(1/2)) or x = -(((3*105^(1/2)+25)^(1/2))/(2*2^(1/2)))

x in { ((3*105^(1/2)+25)^(1/2))/(2*2^(1/2)), -(((3*105^(1/2)+25)^(1/2))/(2*2^(1/2))) }

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