1-5/x=14/x^2

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Solution for 1-5/x=14/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)

1-(5/x) = 14/(x^2) // - 14/(x^2)

1-(5/x)-(14/(x^2)) = 0

1-5*x^-1-14*x^-2 = 0

t_1 = x^-1

1-14*t_1^2-5*t_1^1 = 0

1-14*t_1^2-5*t_1 = 0

DELTA = (-5)^2-(-14*1*4)

DELTA = 81

DELTA > 0

t_1 = (81^(1/2)+5)/(-14*2) or t_1 = (5-81^(1/2))/(-14*2)

t_1 = -1/2 or t_1 = 1/7

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

t_1 = 1/7

x^-1-1/7 = 0

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

x^-1 = 1/7

-1 < 0

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

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

7 = x^1

x = 7

x in { -2, 7 }

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