12x^2=192^2

Solution for 12x^2=192^2 equation:

12x^2=192^2

We move all terms to the left:

12x^2-(192^2)=0

We add all the numbers together, and all the variables

12x^2-36864=0

a = 12; b = 0; c = -36864;
Δ = b2-4ac
Δ = 02-4·12·(-36864)
Δ = 1769472
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:

$\sqrt{\Delta}=\sqrt{1769472}=\sqrt{589824*3}=\sqrt{589824}*\sqrt{3}=768\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-768\sqrt{3}}{2*12}=\frac{0-768\sqrt{3}}{24}
=-\frac{768\sqrt{3}}{24}
=-32\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+768\sqrt{3}}{2*12}=\frac{0+768\sqrt{3}}{24}
=\frac{768\sqrt{3}}{24}
=32\sqrt{3}
$