2n^2=420

Solution for 2n^2=420 equation:

2n^2=420

We move all terms to the left:

2n^2-(420)=0

a = 2; b = 0; c = -420;
Δ = b2-4ac
Δ = 02-4·2·(-420)
Δ = 3360
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:

$\sqrt{\Delta}=\sqrt{3360}=\sqrt{16*210}=\sqrt{16}*\sqrt{210}=4\sqrt{210}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{210}}{2*2}=\frac{0-4\sqrt{210}}{4}
=-\frac{4\sqrt{210}}{4}
=-\sqrt{210}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{210}}{2*2}=\frac{0+4\sqrt{210}}{4}
=\frac{4\sqrt{210}}{4}
=\sqrt{210}
$