(3n)^2=81

Solution for (3n)^2=81 equation:

(3n)^2=81

We move all terms to the left:

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

a = 3; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·3·(-81)
Δ = 972
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{3}}{2*3}=\frac{0-18\sqrt{3}}{6}
=-\frac{18\sqrt{3}}{6}
=-3\sqrt{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{3}}{2*3}=\frac{0+18\sqrt{3}}{6}
=\frac{18\sqrt{3}}{6}
=3\sqrt{3}
$