4x^3-3x-23/27

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Solution for 4x^3-3x-23/27 equation: 


x in (-oo:+oo)

4*x^3-(3*x)-(23/27) = 0

4*x^3-3*x-23/27 = 0

4*x^3-3*x-23/27 = 0

4*x^3-3*x-23/27 = 0 // * 0

{ 1, -1, 23, -23 }

1

x = 1

108*x^3-81*x-23 = 4

1

-1

x = -1

108*x^3-81*x-23 = -50

-1

23

x = 23

108*x^3-81*x-23 = 1312150

23

-23

x = -23

108*x^3-81*x-23 = -1312196

-23

{ 1/2, -1/2, 1/3, -1/3, 1/4, -1/4, 1/6, -1/6, 1/9, -1/9, 1/12, -1/12, 1/18, -1/18, 1/27, -1/27, 1/36, -1/36, 1/54, -1/54, 1/108, -1/108, -1/2, 1/2, -1/3, 1/3, -1/4, 1/4, -1/6, 1/6, -1/9, 1/9, -1/12, 1/12, -1/18, 1/18, -1/27, 1/27, -1/36, 1/36, -1/54, 1/54, -1/108, 1/108, 23/2, -23/2, 23/3, -23/3, 23/4, -23/4, 23/6, -23/6, 23/9, -23/9, 23/12, -23/12, 23/18, -23/18, 23/27, -23/27, 23/36, -23/36, 23/54, -23/54, 23/108, -23/108, -23/2, 23/2, -23/3, 23/3, -23/4, 23/4, -23/6, 23/6, -23/9, 23/9, -23/12, 23/12, -23/18, 23/18, -23/27, 23/27, -23/36, 23/36, -23/54, 23/54, -23/108, 23/108 }

1/2

x

1/2

108*x^3-81*x-23 = -50

1/2

-1/2

x

-1/2

108*x^3-81*x-23 = 4

-1/2

1/3

x

1/3

108*x^3-81*x-23 = -46

1/3

-1/3

x

-1/3

108*x^3-81*x-23 = 0

-1/3

x+1/3

108*x^2-36*x-69

108*x^3-81*x-23

x+1/3

-108*x^3-36*x^2

-36*x^2-81*x-23

36*x^2+12*x

-69*x-23

69*x+23

0

108*x^2-36*x-69 = 0

DELTA = (-36)^2-(-69*4*108)

DELTA = 31104

DELTA > 0

x = (31104^(1/2)+36)/(2*108) or x = (36-31104^(1/2))/(2*108)

x = (72*6^(1/2)+36)/216 or x = (36-72*6^(1/2))/216

x in { (36-72*6^(1/2))/216, (72*6^(1/2)+36)/216, -1/3} 

x in { (36-72*6^(1/2))/216, (72*6^(1/2)+36)/216, -1/3 }

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