0=9x(x-6)-81

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

0=9x(x-6)-81

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(9x(x-6)-81), so:

9x(x-6)-81

We multiply parentheses

9x^2-54x-81

Back to the equation:

-(9x^2-54x-81)


We get rid of 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}
$