(1)-(9/x-3)=-(54/x^2-9)

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Solution for (1)-(9/x-3)=-(54/x^2-9) equation:


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:0) U (0:+oo)

1-(9/x)+3 = -(54/(x^2)-9) // + 54/(x^2)-9

54/(x^2)-(9/x)-9+1+3 = 0

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

54*x^-2-9*x^-1-5 = 0

t_1 = x^-1

54*t_1^2-9*t_1^1-5 = 0

54*t_1^2-9*t_1-5 = 0

DELTA = (-9)^2-(-5*4*54)

DELTA = 1161

DELTA > 0

t_1 = (1161^(1/2)+9)/(2*54) or t_1 = (9-1161^(1/2))/(2*54)

t_1 = (3*129^(1/2)+9)/108 or t_1 = (9-3*129^(1/2))/108

t_1 = (9-3*129^(1/2))/108

x^-1-((9-3*129^(1/2))/108) = 0

1*x^-1 = (9-3*129^(1/2))/108 // : 1

x^-1 = (9-3*129^(1/2))/108

-1 < 0

1/(x^1) = (9-3*129^(1/2))/108 // * x^1

1 = ((9-3*129^(1/2))/108)*x^1 // : (9-3*129^(1/2))/108

108*(9-3*129^(1/2))^-1 = x^1

x = 108*(9-3*129^(1/2))^-1

t_1 = (3*129^(1/2)+9)/108

x^-1-((3*129^(1/2)+9)/108) = 0

1*x^-1 = (3*129^(1/2)+9)/108 // : 1

x^-1 = (3*129^(1/2)+9)/108

-1 < 0

1/(x^1) = (3*129^(1/2)+9)/108 // * x^1

1 = ((3*129^(1/2)+9)/108)*x^1 // : (3*129^(1/2)+9)/108

108*(3*129^(1/2)+9)^-1 = x^1

x = 108*(3*129^(1/2)+9)^-1

x in { 108*(9-3*129^(1/2))^-1, 108*(3*129^(1/2)+9)^-1 }

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