1000=20z^2

Solution for 1000=20z^2 equation:

1000=20z^2

We move all terms to the left:

1000-(20z^2)=0

a = -20; b = 0; c = +1000;
Δ = b2-4ac
Δ = 02-4·(-20)·1000
Δ = 80000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80000}=\sqrt{40000*2}=\sqrt{40000}*\sqrt{2}=200\sqrt{2}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{2}}{2*-20}=\frac{0-200\sqrt{2}}{-40}
=-\frac{200\sqrt{2}}{-40}
=-\frac{5\sqrt{2}}{-1}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{2}}{2*-20}=\frac{0+200\sqrt{2}}{-40}
=\frac{200\sqrt{2}}{-40}
=\frac{5\sqrt{2}}{-1}
$