12n^2=1966080

Solution for 12n^2=1966080 equation:

12n^2=1966080

We move all terms to the left:

12n^2-(1966080)=0

a = 12; b = 0; c = -1966080;
Δ = b2-4ac
Δ = 02-4·12·(-1966080)
Δ = 94371840
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:

$\sqrt{\Delta}=\sqrt{94371840}=\sqrt{9437184*10}=\sqrt{9437184}*\sqrt{10}=3072\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3072\sqrt{10}}{2*12}=\frac{0-3072\sqrt{10}}{24}
=-\frac{3072\sqrt{10}}{24}
=-128\sqrt{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3072\sqrt{10}}{2*12}=\frac{0+3072\sqrt{10}}{24}
=\frac{3072\sqrt{10}}{24}
=128\sqrt{10}
$