z^2-0.5z-0.5=0

Solution for z^2-0.5z-0.5=0 equation:

z^2-0.5z-0.5=0

a = 1; b = -0.5; c = -0.5;
Δ = b2-4ac
Δ = -0.52-4·1·(-0.5)
Δ = 2.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.5)-\sqrt{2.25}}{2*1}=\frac{0.5-\sqrt{2.25}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{2.25}}{2*1}=\frac{0.5+\sqrt{2.25}}{2}
$