x^2=21348

Solution for x^2=21348 equation:

x^2=21348

We move all terms to the left:

x^2-(21348)=0

a = 1; b = 0; c = -21348;
Δ = b2-4ac
Δ = 02-4·1·(-21348)
Δ = 85392
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:

$\sqrt{\Delta}=\sqrt{85392}=\sqrt{144*593}=\sqrt{144}*\sqrt{593}=12\sqrt{593}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{593}}{2*1}=\frac{0-12\sqrt{593}}{2}
=-\frac{12\sqrt{593}}{2}
=-6\sqrt{593}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{593}}{2*1}=\frac{0+12\sqrt{593}}{2}
=\frac{12\sqrt{593}}{2}
=6\sqrt{593}
$