5/x2-1/x=6

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Solution for 5/x2-1/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)

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

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

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

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

t_1 = x^-1

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

5*t_1^2-t_1-6 = 0

DELTA = (-1)^2-(-6*4*5)

DELTA = 121

DELTA > 0

t_1 = (121^(1/2)+1)/(2*5) or t_1 = (1-121^(1/2))/(2*5)

t_1 = 6/5 or t_1 = -1

t_1 = -1

x^-1+1 = 0

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

x^-1 = -1

-1 < 0

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

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

-1 = x^1

x = -1

t_1 = 6/5

x^-1-6/5 = 0

1*x^-1 = 6/5 // : 1

x^-1 = 6/5

-1 < 0

1/(x^1) = 6/5 // * x^1

1 = 6/5*x^1 // : 6/5

5/6 = x^1

x = 5/6

x in { -1, 5/6 }

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