2x^2-82=4x^2-324

Solution for 2x^2-82=4x^2-324 equation:

2x^2-82=4x^2-324

We move all terms to the left:

2x^2-82-(4x^2-324)=0

We get rid of parentheses

2x^2-4x^2+324-82=0

We add all the numbers together, and all the variables

-2x^2+242=0

a = -2; b = 0; c = +242;
Δ = b2-4ac
Δ = 02-4·(-2)·242
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-44}{2*-2}=\frac{-44}{-4}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+44}{2*-2}=\frac{44}{-4}
=-11
$