x^2=1728

Solution for x^2=1728 equation:

x^2=1728

We move all terms to the left:

x^2-(1728)=0

a = 1; b = 0; c = -1728;
Δ = b2-4ac
Δ = 02-4·1·(-1728)
Δ = 6912
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:

$\sqrt{\Delta}=\sqrt{6912}=\sqrt{2304*3}=\sqrt{2304}*\sqrt{3}=48\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{3}}{2*1}=\frac{0-48\sqrt{3}}{2}
=-\frac{48\sqrt{3}}{2}
=-24\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{3}}{2*1}=\frac{0+48\sqrt{3}}{2}
=\frac{48\sqrt{3}}{2}
=24\sqrt{3}
$