1/x^2-1/x-12=0

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Solution for 1/x^2-1/x-12=0 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)-12 = 0

1/(x^2)-x^-1-12 = 0

x^-2-x^-1-12 = 0

t_1 = x^-1

1*t_1^2-1*t_1^1-12 = 0

t_1^2-t_1-12 = 0

DELTA = (-1)^2-(-12*1*4)

DELTA = 49

DELTA > 0

t_1 = (49^(1/2)+1)/(1*2) or t_1 = (1-49^(1/2))/(1*2)

t_1 = 4 or t_1 = -3

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

t_1 = 4

x^-1-4 = 0

1*x^-1 = 4 // : 1

x^-1 = 4

-1 < 0

1/(x^1) = 4 // * x^1

1 = 4*x^1 // : 4

1/4 = x^1

x = 1/4

x in { -1/3, 1/4 }

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