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

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Solution for (77/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)

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

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

x^-1+77/(x^2)-6 = 0

x^-1+77*x^-2-6 = 0

t_1 = x^-1

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

77*t_1^2+t_1-6 = 0

DELTA = 1^2-(-6*4*77)

DELTA = 1849

DELTA > 0

t_1 = (1849^(1/2)-1)/(2*77) or t_1 = (-1849^(1/2)-1)/(2*77)

t_1 = 3/11 or t_1 = -2/7

t_1 = -2/7

x^-1+2/7 = 0

1*x^-1 = -2/7 // : 1

x^-1 = -2/7

-1 < 0

1/(x^1) = -2/7 // * x^1

1 = -2/7*x^1 // : -2/7

-7/2 = x^1

x = -7/2

t_1 = 3/11

x^-1-3/11 = 0

1*x^-1 = 3/11 // : 1

x^-1 = 3/11

-1 < 0

1/(x^1) = 3/11 // * x^1

1 = 3/11*x^1 // : 3/11

11/3 = x^1

x = 11/3

x in { -7/2, 11/3 }

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