2x^2-12+2x^2-12=x^2+24

Solution for 2x^2-12+2x^2-12=x^2+24 equation:

2x^2-12+2x^2-12=x^2+24

We move all terms to the left:

2x^2-12+2x^2-12-(x^2+24)=0

We add all the numbers together, and all the variables

4x^2-(x^2+24)-24=0

We get rid of parentheses

4x^2-x^2-24-24=0

We add all the numbers together, and all the variables

3x^2-48=0

a = 3; b = 0; c = -48;
Δ = b2-4ac
Δ = 02-4·3·(-48)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*3}=\frac{-24}{6}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*3}=\frac{24}{6}
=4
$