9w(81-9w)=81

Solution for 9w(81-9w)=81 equation:

9w(81-9w)=81

We move all terms to the left:

9w(81-9w)-(81)=0

We add all the numbers together, and all the variables

9w(-9w+81)-81=0

We multiply parentheses

-81w^2+729w-81=0

a = -81; b = 729; c = -81;
Δ = b2-4ac
Δ = 7292-4·(-81)·(-81)
Δ = 505197
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{505197}=\sqrt{6561*77}=\sqrt{6561}*\sqrt{77}=81\sqrt{77}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(729)-81\sqrt{77}}{2*-81}=\frac{-729-81\sqrt{77}}{-162}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(729)+81\sqrt{77}}{2*-81}=\frac{-729+81\sqrt{77}}{-162}
$