500=25e^2

Solution for 500=25e^2 equation:

500=25e^2

We move all terms to the left:

500-(25e^2)=0

a = -25; b = 0; c = +500;
Δ = b2-4ac
Δ = 02-4·(-25)·500
Δ = 50000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{50000}=\sqrt{10000*5}=\sqrt{10000}*\sqrt{5}=100\sqrt{5}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{5}}{2*-25}=\frac{0-100\sqrt{5}}{-50}
=-\frac{100\sqrt{5}}{-50}
=-\frac{2\sqrt{5}}{-1}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{5}}{2*-25}=\frac{0+100\sqrt{5}}{-50}
=\frac{100\sqrt{5}}{-50}
=\frac{2\sqrt{5}}{-1}
$