8z^2-2=-8z

Solution for 8z^2-2=-8z equation:

8z^2-2=-8z

We move all terms to the left:

8z^2-2-(-8z)=0

We get rid of parentheses

8z^2+8z-2=0

a = 8; b = 8; c = -2;
Δ = b2-4ac
Δ = 82-4·8·(-2)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{2}}{2*8}=\frac{-8-8\sqrt{2}}{16}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{2}}{2*8}=\frac{-8+8\sqrt{2}}{16}
$