9x(x-6)-81=0

Solution for 9x(x-6)-81=0 equation:

9x(x-6)-81=0

We multiply parentheses

9x^2-54x-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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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