Posted by Kari on Thursday, November 24, 2011 at 1:55am.
This is very effective online webpage.
I simply entered the equation in the form
300x^2 -16.667x^3-7200 = 0
http://www.wolframalpha.com/input/?i=300x%5E2+-16.667x%5E3-7200+%3D0
It gave my 3 real answers and the corresponding gram of
f(x) = 300x^2 -16.667x^3-7200
Let the 16.667 be treated at 16 2/3. Then
900 x^2 -50 x^3 -21600 = 0
One root of that equation is exactly x = 6. Call it a lucky guess.
Divide the cubic by (x-6) to get an easily solved quadratic, for the other two roots. It can be reduced to
x^2 -120 x -72 = 0
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