6X2=76=3x3+8x2-321

Solution for 6X2=76=3x3+8x2-321 equation:

6X^2=76=3X^3+8X^2-321

We move all terms to the left:

6X^2-(76)=0

a = 6; b = 0; c = -76;
Δ = b2-4ac
Δ = 02-4·6·(-76)
Δ = 1824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{114}}{2*6}=\frac{0-4\sqrt{114}}{12}
=-\frac{4\sqrt{114}}{12}
=-\frac{\sqrt{114}}{3}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{114}}{2*6}=\frac{0+4\sqrt{114}}{12}
=\frac{4\sqrt{114}}{12}
=\frac{\sqrt{114}}{3}
$