z*2z=0.5

Solution for z*2z=0.5 equation:

z*2z=0.5

We move all terms to the left:

z*2z-(0.5)=0

We add all the numbers together, and all the variables

z*2z-0.5=0

Wy multiply elements

2z^2-0.5=0

a = 2; b = 0; c = -0.5;
Δ = b2-4ac
Δ = 02-4·2·(-0.5)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2}{2*2}=\frac{-2}{4}
=-1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2}{2*2}=\frac{2}{4}
=1/2
$