



 
Pedro, I don't blame you; while there is a "cubic formula" that will grind out the solutions, it's a bit of a bear and most people try to avoid using it. I suggest the following.
(1) Plot the polynomial for a few easy values, say Other observations (think about these carefully) *There is a negative root, because * The sum of the roots is 17/6 and the product is 12/6. [Why? Expand (xa)(xb)(xc) and look at the coefficients!] Thus if there are three real roots two are positive. This might make positive values a good place to start looking. Good Hunting!
 


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