(n-3)(n-3)=81

Solution for (n-3)(n-3)=81 equation:

(n-3)(n-3)=81

We move all terms to the left:

(n-3)(n-3)-(81)=0

We multiply parentheses ..

(+n^2-3n-3n+9)-81=0

We get rid of parentheses

n^2-3n-3n+9-81=0

We add all the numbers together, and all the variables

n^2-6n-72=0

a = 1; b = -6; c = -72;
Δ = b2-4ac
Δ = -62-4·1·(-72)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18}{2*1}=\frac{-12}{2}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*1}=\frac{24}{2}
=12
$