12=5n^2

Solution for 12=5n^2 equation:

12=5n^2

We move all terms to the left:

12-(5n^2)=0

a = -5; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-5)·12
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*-5}=\frac{0-4\sqrt{15}}{-10}
=-\frac{4\sqrt{15}}{-10}
=-\frac{2\sqrt{15}}{-5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*-5}=\frac{0+4\sqrt{15}}{-10}
=\frac{4\sqrt{15}}{-10}
=\frac{2\sqrt{15}}{-5}
$