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Cubic Equation Cardano solution

  1. Jul 25, 2007 #1
    1. The problem statement, all variables and given/known data
    To solve the following equation
    3x^3 + x^2 + 15x + 27 = 0

    2. Relevant equations

    3. The attempt at a solution

    {(x-> 1/9{-1 - 134/(-3079+27Sqrt.(16305)^(1/2) + (-3079+27Sqrt.(16305)^(1/3)}

    {x-> -1/9 + 67(1+iSqrt.3)/9(-3079+27Sqrt.(16305)^(1/2) -1/18 (1-iSqrt.3)(-3079+27Sqrt.(16305)^(1/2)}

    Is this correct ?

    {x-> -1/9 + 67(1-iSqrt.3)/9(-3079+27Sqrt.(16305)^(1/2) - 1/18 (1+iSqrt.3)(-3079+27Sqrt.(16305)^(1/2)}
  2. jcsd
  3. Jul 25, 2007 #2
    I actually mastered the cubic solution.
    I used this site.
    The methods of Cardano/Tartaglia are trully beautifully derived.
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