z(z=9)=1

Solution for z(z=9)=1 equation:

z(z=9)=1

We move all terms to the left:

z(z-(9))=0

We multiply parentheses

z^2-9z=0

a = 1; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·1·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*1}=\frac{0}{2}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*1}=\frac{18}{2}
=9
$