6/x-5+2/x+5=84/x^2-25

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Solution for 6/x-5+2/x+5=84/x^2-25 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)

6/x+2/x-5+5 = 84/(x^2)-25 // - 84/(x^2)-25

6/x+2/x-(84/(x^2))-5+5+25 = 0

6/x+2/x-84*x^-2-5+5+25 = 0

8*x^-1-84*x^-2+25 = 0

t_1 = x^-1

8*t_1^1-84*t_1^2+25 = 0

8*t_1-84*t_1^2+25 = 0

DELTA = 8^2-(-84*4*25)

DELTA = 8464

DELTA > 0

t_1 = (8464^(1/2)-8)/(-84*2) or t_1 = (-8464^(1/2)-8)/(-84*2)

t_1 = -1/2 or t_1 = 25/42

t_1 = -1/2

x^-1+1/2 = 0

1*x^-1 = -1/2 // : 1

x^-1 = -1/2

-1 < 0

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

1 = -1/2*x^1 // : -1/2

-2 = x^1

x = -2

t_1 = 25/42

x^-1-25/42 = 0

1*x^-1 = 25/42 // : 1

x^-1 = 25/42

-1 < 0

1/(x^1) = 25/42 // * x^1

1 = 25/42*x^1 // : 25/42

42/25 = x^1

x = 42/25

x in { -2, 42/25 }

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