-9z(z-9)=0

Solution for -9z(z-9)=0 equation:

-9z(z-9)=0

We multiply parentheses

-9z^2+81z=0

a = -9; b = 81; c = 0;
Δ = b2-4ac
Δ = 812-4·(-9)·0
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-81}{2*-9}=\frac{-162}{-18}
=+9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+81}{2*-9}=\frac{0}{-18}
=0
$