5/x^2-38/x=16

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Solution for 5/x^2-38/x=16 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)-(38/x) = 16 // - 16

5/(x^2)-(38/x)-16 = 0

5/(x^2)-38*x^-1-16 = 0

5*x^-2-38*x^-1-16 = 0

t_1 = x^-1

5*t_1^2-38*t_1^1-16 = 0

5*t_1^2-38*t_1-16 = 0

DELTA = (-38)^2-(-16*4*5)

DELTA = 1764

DELTA > 0

t_1 = (1764^(1/2)+38)/(2*5) or t_1 = (38-1764^(1/2))/(2*5)

t_1 = 8 or t_1 = -2/5

t_1 = -2/5

x^-1+2/5 = 0

1*x^-1 = -2/5 // : 1

x^-1 = -2/5

-1 < 0

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

1 = -2/5*x^1 // : -2/5

-5/2 = x^1

x = -5/2

t_1 = 8

x^-1-8 = 0

1*x^-1 = 8 // : 1

x^-1 = 8

-1 < 0

1/(x^1) = 8 // * x^1

1 = 8*x^1 // : 8

1/8 = x^1

x = 1/8

x in { -5/2, 1/8 }

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