1000=e^2*16

Solution for 1000=e^2*16 equation:

1000=e^2*16

We move all terms to the left:

1000-(e^2*16)=0

We get rid of parentheses

-e^2*16+1000=0

Wy multiply elements

-16e^2+1000=0

a = -16; b = 0; c = +1000;
Δ = b2-4ac
Δ = 02-4·(-16)·1000
Δ = 64000
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:

$\sqrt{\Delta}=\sqrt{64000}=\sqrt{6400*10}=\sqrt{6400}*\sqrt{10}=80\sqrt{10}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{10}}{2*-16}=\frac{0-80\sqrt{10}}{-32}
=-\frac{80\sqrt{10}}{-32}
=-\frac{5\sqrt{10}}{-2}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{10}}{2*-16}=\frac{0+80\sqrt{10}}{-32}
=\frac{80\sqrt{10}}{-32}
=\frac{5\sqrt{10}}{-2}
$