How do I find roots of the 3rd order polynomial?

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$$5x^3 - 21x^2 - 11x + 3 = 0$$

I am not allowed to use a graphical calculator on the exam

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Either use numerical methods, or graphing calculator, or if you want exact form

see The Cubic Formula, by the way it's too complicated to remember or to evaluate by hand.

I would suggest using Wolfy for this purpose.