x^2=3072

Solution for x^2=3072 equation:

x^2=3072

We move all terms to the left:

x^2-(3072)=0

a = 1; b = 0; c = -3072;
Δ = b2-4ac
Δ = 02-4·1·(-3072)
Δ = 12288
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:

$\sqrt{\Delta}=\sqrt{12288}=\sqrt{4096*3}=\sqrt{4096}*\sqrt{3}=64\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{3}}{2*1}=\frac{0-64\sqrt{3}}{2}
=-\frac{64\sqrt{3}}{2}
=-32\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{3}}{2*1}=\frac{0+64\sqrt{3}}{2}
=\frac{64\sqrt{3}}{2}
=32\sqrt{3}
$