(1/x^2)-(1/x)=6

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Solution for (1/x^2)-(1/x)=6 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^2)-(1/x) = 6 // - 6

1/(x^2)-(1/x)-6 = 0

1/(x^2)-x^-1-6 = 0

x^-2-x^-1-6 = 0

t_1 = x^-1

1*t_1^2-1*t_1^1-6 = 0

t_1^2-t_1-6 = 0

DELTA = (-1)^2-(-6*1*4)

DELTA = 25

DELTA > 0

t_1 = (25^(1/2)+1)/(1*2) or t_1 = (1-25^(1/2))/(1*2)

t_1 = 3 or t_1 = -2

t_1 = -2

x^-1+2 = 0

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

x^-1 = -2

-1 < 0

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

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

-1/2 = x^1

x = -1/2

t_1 = 3

x^-1-3 = 0

1*x^-1 = 3 // : 1

x^-1 = 3

-1 < 0

1/(x^1) = 3 // * x^1

1 = 3*x^1 // : 3

1/3 = x^1

x = 1/3

x in { -1/2, 1/3 }

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