(5/x^2)-(54/x)=11

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Solution for (5/x^2)-(54/x)=11 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)-(54/x) = 11 // - 11

5/(x^2)-(54/x)-11 = 0

5/(x^2)-54*x^-1-11 = 0

5*x^-2-54*x^-1-11 = 0

t_1 = x^-1

5*t_1^2-54*t_1^1-11 = 0

5*t_1^2-54*t_1-11 = 0

DELTA = (-54)^2-(-11*4*5)

DELTA = 3136

DELTA > 0

t_1 = (3136^(1/2)+54)/(2*5) or t_1 = (54-3136^(1/2))/(2*5)

t_1 = 11 or t_1 = -1/5

t_1 = -1/5

x^-1+1/5 = 0

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

x^-1 = -1/5

-1 < 0

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

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

-5 = x^1

x = -5

t_1 = 11

x^-1-11 = 0

1*x^-1 = 11 // : 1

x^-1 = 11

-1 < 0

1/(x^1) = 11 // * x^1

1 = 11*x^1 // : 11

1/11 = x^1

x = 1/11

x in { -5, 1/11 }

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