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

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Solution for (5/x)=(6/x^2)+1 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 = 6/(x^2)+1 // - 6/(x^2)+1

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

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

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

t_1 = x^-1

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

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

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

DELTA = 1

DELTA > 0

t_1 = (1^(1/2)-5)/(-6*2) or t_1 = (-1^(1/2)-5)/(-6*2)

t_1 = 1/3 or t_1 = 1/2

t_1 = 1/3

x^-1-1/3 = 0

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

x^-1 = 1/3

-1 < 0

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

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

3 = x^1

x = 3

t_1 = 1/2

x^-1-1/2 = 0

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

x^-1 = 1/2

-1 < 0

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

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

2 = x^1

x = 2

x in { 3, 2 }

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