25x^2-4/x^2-9

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Solution for 25x^2-4/x^2-9 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)

25*x^2-(4/(x^2))-9 = 0

25*x^2-4*x^-2-9 = 0

t_1 = x^2

25*t_1^1-4*t_1^-1-9 = 0

25*t_1^1-4*t_1^-1-9*t_1^0 = 0

(25*t_1^2-9*t_1^1-4*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(25*t_1^2-9*t_1^1-4*t_1^0) = 0

t_1^1

25*t_1^2-9*t_1-4 = 0

25*t_1^2-9*t_1-4 = 0

DELTA = (-9)^2-(-4*4*25)

DELTA = 481

DELTA > 0

t_1 = (481^(1/2)+9)/(2*25) or t_1 = (9-481^(1/2))/(2*25)

t_1 = (481^(1/2)+9)/50 or t_1 = (9-481^(1/2))/50

t_1 in { (9-481^(1/2))/50, (481^(1/2)+9)/50} 

t_1 = (9-481^(1/2))/50

x^2-((9-481^(1/2))/50) = 0

1*x^2 = (9-481^(1/2))/50 // : 1

x^2 = (9-481^(1/2))/50

t_1 = (481^(1/2)+9)/50

x^2-((481^(1/2)+9)/50) = 0

1*x^2 = (481^(1/2)+9)/50 // : 1

x^2 = (481^(1/2)+9)/50

x^2 = (481^(1/2)+9)/50 // ^ 1/2

abs(x) = ((481^(1/2)+9)^(1/2))/(5*2^(1/2))

x = ((481^(1/2)+9)^(1/2))/(5*2^(1/2)) or x = -(((481^(1/2)+9)^(1/2))/(5*2^(1/2)))

x in { ((481^(1/2)+9)^(1/2))/(5*2^(1/2)), -(((481^(1/2)+9)^(1/2))/(5*2^(1/2))) }

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