0.2-0.1z^2=z

Solution for 0.2-0.1z^2=z equation:

0.2-0.1z^2=z

We move all terms to the left:

0.2-0.1z^2-(z)=0

We add all the numbers together, and all the variables

-0.1z^2-1z+0.2=0

a = -0.1; b = -1; c = +0.2;
Δ = b2-4ac
Δ = -12-4·(-0.1)·0.2
Δ = 1.08
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{-(-1)-\sqrt{1.08}}{2*-0.1}=\frac{1-\sqrt{1.08}}{-0.2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1.08}}{2*-0.1}=\frac{1+\sqrt{1.08}}{-0.2}
$