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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+245=0

a = -2; b = 0; c = +245;
Δ = b2-4ac
Δ = 02-4·(-2)·245
Δ = 1960
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:

$\sqrt{\Delta}=\sqrt{1960}=\sqrt{196*10}=\sqrt{196}*\sqrt{10}=14\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{10}}{2*-2}=\frac{0-14\sqrt{10}}{-4}
=-\frac{14\sqrt{10}}{-4}
=-\frac{7\sqrt{10}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{10}}{2*-2}=\frac{0+14\sqrt{10}}{-4}
=\frac{14\sqrt{10}}{-4}
=\frac{7\sqrt{10}}{-2}
$