1,000=20z2

Solution for 1,000=20z2 equation:

1.000=20z^2

We move all terms to the left:

1.000-(20z^2)=0

We add all the numbers together, and all the variables

-20z^2+1=0

a = -20; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-20)·1
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*-20}=\frac{0-4\sqrt{5}}{-40}
=-\frac{4\sqrt{5}}{-40}
=-\frac{\sqrt{5}}{-10}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*-20}=\frac{0+4\sqrt{5}}{-40}
=\frac{4\sqrt{5}}{-40}
=\frac{\sqrt{5}}{-10}
$