-1/x-6/x^2=-12

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Solution for -1/x-6/x^2=-12 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-(6/(x^2)) = -12 // + 12

12-1/x-(6/(x^2)) = 0

12-1/x-6*x^-2 = 0

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

t_1 = x^-1

12-6*t_1^2-1*t_1^1 = 0

12-6*t_1^2-t_1 = 0

DELTA = (-1)^2-(-6*4*12)

DELTA = 289

DELTA > 0

t_1 = (289^(1/2)+1)/(-6*2) or t_1 = (1-289^(1/2))/(-6*2)

t_1 = -3/2 or t_1 = 4/3

t_1 = -3/2

x^-1+3/2 = 0

1*x^-1 = -3/2 // : 1

x^-1 = -3/2

-1 < 0

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

1 = -3/2*x^1 // : -3/2

-2/3 = x^1

x = -2/3

t_1 = 4/3

x^-1-4/3 = 0

1*x^-1 = 4/3 // : 1

x^-1 = 4/3

-1 < 0

1/(x^1) = 4/3 // * x^1

1 = 4/3*x^1 // : 4/3

3/4 = x^1

x = 3/4

x in { -2/3, 3/4 }

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