Maximum possible integer square root polynomial 2: Much harder

Find the maximum possible integral value of

$\sqrt{a^2x^2+bx+c}$

Where $${a,b,c,x}$$ are integers, $${a^2,b,c}<3000$$; $${a,b,c,x}>0$$; and b is odd.

You may use a calculator. I encourage you to use only a pencil and a hand held calculator because that is how I did it. There is no shame in using wolfram alpha FOR CALCULATIONS because the numbers do get quite large.

the easier version of this is here

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