n^2/3=216

Solution for n^2/3=216 equation:

n^2/3=216

We move all terms to the left:

n^2/3-(216)=0

We multiply all the terms by the denominator


n^2-216*3=0

We add all the numbers together, and all the variables

n^2-648=0

a = 1; b = 0; c = -648;
Δ = b2-4ac
Δ = 02-4·1·(-648)
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{2}}{2*1}=\frac{0-36\sqrt{2}}{2}
=-\frac{36\sqrt{2}}{2}
=-18\sqrt{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{2}}{2*1}=\frac{0+36\sqrt{2}}{2}
=\frac{36\sqrt{2}}{2}
=18\sqrt{2}
$