n^2+n^2+n^2=30

Solution for n^2+n^2+n^2=30 equation:

n^2+n^2+n^2=30

We move all terms to the left:

n^2+n^2+n^2-(30)=0

We add all the numbers together, and all the variables

3n^2-30=0

a = 3; b = 0; c = -30;
Δ = b2-4ac
Δ = 02-4·3·(-30)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{10}}{2*3}=\frac{0-6\sqrt{10}}{6}
=-\frac{6\sqrt{10}}{6}
=-\sqrt{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{10}}{2*3}=\frac{0+6\sqrt{10}}{6}
=\frac{6\sqrt{10}}{6}
=\sqrt{10}
$