3+2/x=65/x^2

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Solution for 3+2/x=65/x^2 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)

2/x+3 = 65/(x^2) // - 65/(x^2)

2/x-(65/(x^2))+3 = 0

2/x-65*x^-2+3 = 0

2*x^-1-65*x^-2+3 = 0

t_1 = x^-1

2*t_1^1-65*t_1^2+3 = 0

2*t_1-65*t_1^2+3 = 0

DELTA = 2^2-(-65*3*4)

DELTA = 784

DELTA > 0

t_1 = (784^(1/2)-2)/(-65*2) or t_1 = (-784^(1/2)-2)/(-65*2)

t_1 = -1/5 or t_1 = 3/13

t_1 = -1/5

x^-1+1/5 = 0

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

x^-1 = -1/5

-1 < 0

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

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

-5 = x^1

x = -5

t_1 = 3/13

x^-1-3/13 = 0

1*x^-1 = 3/13 // : 1

x^-1 = 3/13

-1 < 0

1/(x^1) = 3/13 // * x^1

1 = 3/13*x^1 // : 3/13

13/3 = x^1

x = 13/3

x in { -5, 13/3 }

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