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

Solution for 6^2-76=3x^2+8x^2-321 equation:

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

We move all terms to the left:

6^2-76-(3x^2+8x^2-321)=0

We add all the numbers together, and all the variables

-(3x^2+8x^2-321)-40=0

We get rid of parentheses

-3x^2-8x^2+321-40=0

We add all the numbers together, and all the variables

-11x^2+281=0

a = -11; b = 0; c = +281;
Δ = b2-4ac
Δ = 02-4·(-11)·281
Δ = 12364
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:

$\sqrt{\Delta}=\sqrt{12364}=\sqrt{4*3091}=\sqrt{4}*\sqrt{3091}=2\sqrt{3091}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3091}}{2*-11}=\frac{0-2\sqrt{3091}}{-22}
=-\frac{2\sqrt{3091}}{-22}
=-\frac{\sqrt{3091}}{-11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3091}}{2*-11}=\frac{0+2\sqrt{3091}}{-22}
=\frac{2\sqrt{3091}}{-22}
=\frac{\sqrt{3091}}{-11}
$