14/x^2-5/x=1

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Solution for 14/x^2-5/x=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)

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

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

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

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

t_1 = x^-1

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

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

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

DELTA = 81

DELTA > 0

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

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

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

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 { -7, 2 }

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