n^2=4590

Solution for n^2=4590 equation:

n^2=4590

We move all terms to the left:

n^2-(4590)=0

a = 1; b = 0; c = -4590;
Δ = b2-4ac
Δ = 02-4·1·(-4590)
Δ = 18360
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:

$\sqrt{\Delta}=\sqrt{18360}=\sqrt{36*510}=\sqrt{36}*\sqrt{510}=6\sqrt{510}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{510}}{2*1}=\frac{0-6\sqrt{510}}{2}
=-\frac{6\sqrt{510}}{2}
=-3\sqrt{510}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{510}}{2*1}=\frac{0+6\sqrt{510}}{2}
=\frac{6\sqrt{510}}{2}
=3\sqrt{510}
$