5/x^2+5=26/x

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Solution for 5/x^2+5=26/x 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)

5/(x^2)+5 = 26/x // - 26/x

5/(x^2)-(26/x)+5 = 0

5/(x^2)-26*x^-1+5 = 0

5*x^-2-26*x^-1+5 = 0

t_1 = x^-1

5*t_1^2-26*t_1^1+5 = 0

5*t_1^2-26*t_1+5 = 0

DELTA = (-26)^2-(4*5*5)

DELTA = 576

DELTA > 0

t_1 = (576^(1/2)+26)/(2*5) or t_1 = (26-576^(1/2))/(2*5)

t_1 = 5 or t_1 = 1/5

t_1 = 1/5

x^-1-1/5 = 0

1*x^-1 = 1/5 // : 1

x^-1 = 1/5

-1 < 0

1/(x^1) = 1/5 // * x^1

1 = 1/5*x^1 // : 1/5

5 = x^1

x = 5

t_1 = 5

x^-1-5 = 0

1*x^-1 = 5 // : 1

x^-1 = 5

-1 < 0

1/(x^1) = 5 // * x^1

1 = 5*x^1 // : 5

1/5 = x^1

x = 1/5

x in { 5, 1/5 }

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