9z(z-6)=81

Solution for 9z(z-6)=81 equation:

9z(z-6)=81

We move all terms to the left:

9z(z-6)-(81)=0

We multiply parentheses

9z^2-54z-81=0

a = 9; b = -54; c = -81;
Δ = b2-4ac
Δ = -542-4·9·(-81)
Δ = 5832
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5832}=\sqrt{2916*2}=\sqrt{2916}*\sqrt{2}=54\sqrt{2}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-54\sqrt{2}}{2*9}=\frac{54-54\sqrt{2}}{18}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+54\sqrt{2}}{2*9}=\frac{54+54\sqrt{2}}{18}
$