9(n-9)(n-9)=16

Solution for 9(n-9)(n-9)=16 equation:

9(n-9)(n-9)=16

We move all terms to the left:

9(n-9)(n-9)-(16)=0

We multiply parentheses ..

9(+n^2-9n-9n+81)-16=0

We multiply parentheses

9n^2-81n-81n+729-16=0

We add all the numbers together, and all the variables

9n^2-162n+713=0

a = 9; b = -162; c = +713;
Δ = b2-4ac
Δ = -1622-4·9·713
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-24}{2*9}=\frac{138}{18}
=7+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+24}{2*9}=\frac{186}{18}
=10+1/3
$