3/x^2-47/x=16

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Solution for 3/x^2-47/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)

3/(x^2)-(47/x) = 16 // - 16

3/(x^2)-(47/x)-16 = 0

3/(x^2)-47*x^-1-16 = 0

3*x^-2-47*x^-1-16 = 0

t_1 = x^-1

3*t_1^2-47*t_1^1-16 = 0

3*t_1^2-47*t_1-16 = 0

DELTA = (-47)^2-(-16*3*4)

DELTA = 2401

DELTA > 0

t_1 = (2401^(1/2)+47)/(2*3) or t_1 = (47-2401^(1/2))/(2*3)

t_1 = 16 or t_1 = -1/3

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 = 16

x^-1-16 = 0

1*x^-1 = 16 // : 1

x^-1 = 16

-1 < 0

1/(x^1) = 16 // * x^1

1 = 16*x^1 // : 16

1/16 = x^1

x = 1/16

x in { -3, 1/16 }

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