x^2=82496

Solution for x^2=82496 equation:

x^2=82496

We move all terms to the left:

x^2-(82496)=0

a = 1; b = 0; c = -82496;
Δ = b2-4ac
Δ = 02-4·1·(-82496)
Δ = 329984
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:

$\sqrt{\Delta}=\sqrt{329984}=\sqrt{256*1289}=\sqrt{256}*\sqrt{1289}=16\sqrt{1289}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{1289}}{2*1}=\frac{0-16\sqrt{1289}}{2}
=-\frac{16\sqrt{1289}}{2}
=-8\sqrt{1289}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{1289}}{2*1}=\frac{0+16\sqrt{1289}}{2}
=\frac{16\sqrt{1289}}{2}
=8\sqrt{1289}
$