3x^2=81/x

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Solution for 3x^2=81/x equation: 


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

3*x^2 = 81/x // - 81/x

3*x^2-(81/x) = 0

3*x^2-81*x^-1 = 0

3*x^2-81*x^-1 = 0

(3*x^3-81*x^0)/(x^1) = 0 // * x^2

x^1*(3*x^3-81*x^0) = 0

x^1

3*x^3-81 = 0

{ 1, -1, 3, -3, 9, -9, 27, -27, 81, -81 }

1

x = 1

3*x^3-81 = -78

1

-1

x = -1

3*x^3-81 = -84

-1

3

x = 3

3*x^3-81 = 0

3

x-3

3*x^2+9*x+27

3*x^3-81

x-3

9*x^2-3*x^3

9*x^2-81

27*x-9*x^2

27*x-81

81-27*x

0

3*x^2+9*x+27 = 0

DELTA = 9^2-(3*4*27)

DELTA = -243

DELTA < 0

x in { 3} 

x = 3

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