d^2=2400

Solution for d^2=2400 equation:

d^2=2400

We move all terms to the left:

d^2-(2400)=0

a = 1; b = 0; c = -2400;
Δ = b2-4ac
Δ = 02-4·1·(-2400)
Δ = 9600
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:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{6}}{2*1}=\frac{0-40\sqrt{6}}{2}
=-\frac{40\sqrt{6}}{2}
=-20\sqrt{6}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{6}}{2*1}=\frac{0+40\sqrt{6}}{2}
=\frac{40\sqrt{6}}{2}
=20\sqrt{6}
$