(4/x-7)-(5/x+7)=(2/x^2-49)

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Solution for (4/x-7)-(5/x+7)=(2/x^2-49) 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)

4/x-(5/x)-7-7 = 2/(x^2)-49 // - 2/(x^2)-49

4/x-(5/x)-(2/(x^2))-7-7+49 = 0

4/x-5*x^-1-2*x^-2-7-7+49 = 0

35-x^-1-2*x^-2 = 0

t_1 = x^-1

35-2*t_1^2-1*t_1^1 = 0

35-2*t_1^2-t_1 = 0

DELTA = (-1)^2-(-2*4*35)

DELTA = 281

DELTA > 0

t_1 = (281^(1/2)+1)/(-2*2) or t_1 = (1-281^(1/2))/(-2*2)

t_1 = (281^(1/2)+1)/(-4) or t_1 = (1-281^(1/2))/(-4)

t_1 = (281^(1/2)+1)/(-4)

x^-1-((281^(1/2)+1)/(-4)) = 0

1*x^-1 = (281^(1/2)+1)/(-4) // : 1

x^-1 = (281^(1/2)+1)/(-4)

-1 < 0

1/(x^1) = (281^(1/2)+1)/(-4) // * x^1

1 = ((281^(1/2)+1)/(-4))*x^1 // : (281^(1/2)+1)/(-4)

-4*(281^(1/2)+1)^-1 = x^1

x = -4*(281^(1/2)+1)^-1

t_1 = (1-281^(1/2))/(-4)

x^-1-((1-281^(1/2))/(-4)) = 0

1*x^-1 = (1-281^(1/2))/(-4) // : 1

x^-1 = (1-281^(1/2))/(-4)

-1 < 0

1/(x^1) = (1-281^(1/2))/(-4) // * x^1

1 = ((1-281^(1/2))/(-4))*x^1 // : (1-281^(1/2))/(-4)

-4*(1-281^(1/2))^-1 = x^1

x = -4*(1-281^(1/2))^-1

x in { -4*(281^(1/2)+1)^-1, -4*(1-281^(1/2))^-1 }

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