(X^3-6x^2-21x-18)/(2x-1)

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Solution for (X^3-6x^2-21x-18)/(2x-1) equation: 


D( x )

2*x-1 = 0

2*x-1 = 0

2*x-1 = 0

2*x-1 = 0 // + 1

2*x = 1 // : 2

x = 1/2

x in (-oo:1/2) U (1/2:+oo)

(X^3-(6*x^2)-(21*x)-18)/(2*x-1) = 0

(X^3-6*x^2-21*x-18)/(2*x-1) = 0

X^3-6*x^2-21*x-18 = 0

DELTA = (-21)^2-(-6*4*(X^3-18))

DELTA = 24*(X^3-18)+441

24*(X^3-18)+441 = 0

24*(X^3-18)+441 = 0

24*X^3+9 = 0

24*X^3+9 = 0

24*X^3 = -9 // : 24

X^3 = -3/8

X^3 = -3/8 // ^ 1/3

X = -(3/8)^(1/3)

DELTA = 0  <=>  t_2 = -(3/8)^(1/3)

x = 21/(-6*2) i X = -(3/8)^(1/3)

x = -7/4 i X = -(3/8)^(1/3)

( x = ((24*(X^3-18)+441)^(1/2)+21)/(-6*2) or x = (21-(24*(X^3-18)+441)^(1/2))/(-6*2) ) i X > -(3/8)^(1/3)

( x = ((24*(X^3-18)+441)^(1/2)+21)/(-12) or x = (21-(24*(X^3-18)+441)^(1/2))/(-12) ) i X > -(3/8)^(1/3)

X+(3/8)^(1/3) > 0

X+(3/8)^(1/3) > 0 // - (3/8)^(1/3)

X > -(3/8)^(1/3)

x in { -7/4, ((24*(X^3-18)+441)^(1/2)+21)/(-12), (21-(24*(X^3-18)+441)^(1/2))/(-12) }

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