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

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

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

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

t_1 = x^-1

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

t_1-6*t_1^2+12 = 0

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

DELTA = 289

DELTA > 0

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

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

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

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

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

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