2x^2-54/x^2-9

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Solution for 2x^2-54/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)

2*x^2-(54/(x^2))-9 = 0

2*x^2-54*x^-2-9 = 0

t_1 = x^2

2*t_1^1-54*t_1^-1-9 = 0

2*t_1^1-54*t_1^-1-9*t_1^0 = 0

(2*t_1^2-9*t_1^1-54*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(2*t_1^2-9*t_1^1-54*t_1^0) = 0

t_1^1

2*t_1^2-9*t_1-54 = 0

2*t_1^2-9*t_1-54 = 0

DELTA = (-9)^2-(-54*2*4)

DELTA = 513

DELTA > 0

t_1 = (513^(1/2)+9)/(2*2) or t_1 = (9-513^(1/2))/(2*2)

t_1 = (3*57^(1/2)+9)/4 or t_1 = (9-3*57^(1/2))/4

t_1 in { (9-3*57^(1/2))/4, (3*57^(1/2)+9)/4} 

t_1 = (9-3*57^(1/2))/4

x^2-((9-3*57^(1/2))/4) = 0

1*x^2 = (9-3*57^(1/2))/4 // : 1

x^2 = (9-3*57^(1/2))/4

t_1 = (3*57^(1/2)+9)/4

x^2-((3*57^(1/2)+9)/4) = 0

1*x^2 = (3*57^(1/2)+9)/4 // : 1

x^2 = (3*57^(1/2)+9)/4

x^2 = (3*57^(1/2)+9)/4 // ^ 1/2

abs(x) = ((3*57^(1/2)+9)^(1/2))/2

x = ((3*57^(1/2)+9)^(1/2))/2 or x = -(((3*57^(1/2)+9)^(1/2))/2)

x in { ((3*57^(1/2)+9)^(1/2))/2, -(((3*57^(1/2)+9)^(1/2))/2) }

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