d^2=3200

Solution for d^2=3200 equation:

d^2=3200

We move all terms to the left:

d^2-(3200)=0

a = 1; b = 0; c = -3200;
Δ = b2-4ac
Δ = 02-4·1·(-3200)
Δ = 12800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12800}=\sqrt{6400*2}=\sqrt{6400}*\sqrt{2}=80\sqrt{2}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{2}}{2*1}=\frac{0-80\sqrt{2}}{2}
=-\frac{80\sqrt{2}}{2}
=-40\sqrt{2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{2}}{2*1}=\frac{0+80\sqrt{2}}{2}
=\frac{80\sqrt{2}}{2}
=40\sqrt{2}
$