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

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

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

We move all terms to the left:

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

We use the square of the difference formula

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5x^2+245=0

a = -5; b = 0; c = +245;
Δ = b2-4ac
Δ = 02-4·(-5)·245
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-70}{2*-5}=\frac{-70}{-10}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+70}{2*-5}=\frac{70}{-10}
=-7
$