12^2=3x^2-x^2

Solution for 12^2=3x^2-x^2 equation:

12^2=3x^2-x^2

We move all terms to the left:

12^2-(3x^2-x^2)=0

We add all the numbers together, and all the variables

-(3x^2-x^2)+144=0

We get rid of parentheses

-3x^2+x^2+144=0

We add all the numbers together, and all the variables

-2x^2+144=0

a = -2; b = 0; c = +144;
Δ = b2-4ac
Δ = 02-4·(-2)·144
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*-2}=\frac{0-24\sqrt{2}}{-4}
=-\frac{24\sqrt{2}}{-4}
=-\frac{6\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*-2}=\frac{0+24\sqrt{2}}{-4}
=\frac{24\sqrt{2}}{-4}
=\frac{6\sqrt{2}}{-1}
$