n^2=1440

Solution for n^2=1440 equation:

n^2=1440

We move all terms to the left:

n^2-(1440)=0

a = 1; b = 0; c = -1440;
Δ = b2-4ac
Δ = 02-4·1·(-1440)
Δ = 5760
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:

$\sqrt{\Delta}=\sqrt{5760}=\sqrt{576*10}=\sqrt{576}*\sqrt{10}=24\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{10}}{2*1}=\frac{0-24\sqrt{10}}{2}
=-\frac{24\sqrt{10}}{2}
=-12\sqrt{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{10}}{2*1}=\frac{0+24\sqrt{10}}{2}
=\frac{24\sqrt{10}}{2}
=12\sqrt{10}
$