x^2=32000

Solution for x^2=32000 equation:

x^2=32000

We move all terms to the left:

x^2-(32000)=0

a = 1; b = 0; c = -32000;
Δ = b2-4ac
Δ = 02-4·1·(-32000)
Δ = 128000
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:

$\sqrt{\Delta}=\sqrt{128000}=\sqrt{25600*5}=\sqrt{25600}*\sqrt{5}=160\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-160\sqrt{5}}{2*1}=\frac{0-160\sqrt{5}}{2}
=-\frac{160\sqrt{5}}{2}
=-80\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+160\sqrt{5}}{2*1}=\frac{0+160\sqrt{5}}{2}
=\frac{160\sqrt{5}}{2}
=80\sqrt{5}
$