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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+236=0

a = -2; b = 0; c = +236;
Δ = b2-4ac
Δ = 02-4·(-2)·236
Δ = 1888
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:

$\sqrt{\Delta}=\sqrt{1888}=\sqrt{16*118}=\sqrt{16}*\sqrt{118}=4\sqrt{118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{118}}{2*-2}=\frac{0-4\sqrt{118}}{-4}
=-\frac{4\sqrt{118}}{-4}
=-\frac{\sqrt{118}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{118}}{2*-2}=\frac{0+4\sqrt{118}}{-4}
=\frac{4\sqrt{118}}{-4}
=\frac{\sqrt{118}}{-1}
$