50=8z^2

Solution for 50=8z^2 equation:

50=8z^2

We move all terms to the left:

50-(8z^2)=0

a = -8; b = 0; c = +50;
Δ = b2-4ac
Δ = 02-4·(-8)·50
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40}{2*-8}=\frac{-40}{-16}
=2+1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40}{2*-8}=\frac{40}{-16}
=-2+1/2
$