(3/x^2)-(53/x)=18

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Solution for (3/x^2)-(53/x)=18 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)-(53/x) = 18 // - 18

3/(x^2)-(53/x)-18 = 0

3/(x^2)-53*x^-1-18 = 0

3*x^-2-53*x^-1-18 = 0

t_1 = x^-1

3*t_1^2-53*t_1^1-18 = 0

3*t_1^2-53*t_1-18 = 0

DELTA = (-53)^2-(-18*3*4)

DELTA = 3025

DELTA > 0

t_1 = (3025^(1/2)+53)/(2*3) or t_1 = (53-3025^(1/2))/(2*3)

t_1 = 18 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 = 18

x^-1-18 = 0

1*x^-1 = 18 // : 1

x^-1 = 18

-1 < 0

1/(x^1) = 18 // * x^1

1 = 18*x^1 // : 18

1/18 = x^1

x = 1/18

x in { -3, 1/18 }

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