1/x-5=10/x^2-25

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Solution for 1/x-5=10/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)

1/x-5 = 10/(x^2)-25 // - 10/(x^2)-25

1/x-(10/(x^2))-5+25 = 0

1/x-10*x^-2-5+25 = 0

x^-1-10*x^-2+20 = 0

t_1 = x^-1

1*t_1^1-10*t_1^2+20 = 0

t_1-10*t_1^2+20 = 0

DELTA = 1^2-(-10*4*20)

DELTA = 801

DELTA > 0

t_1 = (801^(1/2)-1)/(-10*2) or t_1 = (-801^(1/2)-1)/(-10*2)

t_1 = (3*89^(1/2)-1)/(-20) or t_1 = (-3*89^(1/2)-1)/(-20)

t_1 = (3*89^(1/2)-1)/(-20)

x^-1-((3*89^(1/2)-1)/(-20)) = 0

1*x^-1 = (3*89^(1/2)-1)/(-20) // : 1

x^-1 = (3*89^(1/2)-1)/(-20)

-1 < 0

1/(x^1) = (3*89^(1/2)-1)/(-20) // * x^1

1 = ((3*89^(1/2)-1)/(-20))*x^1 // : (3*89^(1/2)-1)/(-20)

-20*(3*89^(1/2)-1)^-1 = x^1

x = -20*(3*89^(1/2)-1)^-1

t_1 = (-3*89^(1/2)-1)/(-20)

x^-1-((-3*89^(1/2)-1)/(-20)) = 0

1*x^-1 = (-3*89^(1/2)-1)/(-20) // : 1

x^-1 = (-3*89^(1/2)-1)/(-20)

-1 < 0

1/(x^1) = (-3*89^(1/2)-1)/(-20) // * x^1

1 = ((-3*89^(1/2)-1)/(-20))*x^1 // : (-3*89^(1/2)-1)/(-20)

-20*(-3*89^(1/2)-1)^-1 = x^1

x = -20*(-3*89^(1/2)-1)^-1

x in { -20*(3*89^(1/2)-1)^-1, -20*(-3*89^(1/2)-1)^-1 }

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