10n^2+1=721

Solution for 10n^2+1=721 equation:

10n^2+1=721

We move all terms to the left:

10n^2+1-(721)=0

We add all the numbers together, and all the variables

10n^2-720=0

a = 10; b = 0; c = -720;
Δ = b2-4ac
Δ = 02-4·10·(-720)
Δ = 28800
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:

$\sqrt{\Delta}=\sqrt{28800}=\sqrt{14400*2}=\sqrt{14400}*\sqrt{2}=120\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120\sqrt{2}}{2*10}=\frac{0-120\sqrt{2}}{20}
=-\frac{120\sqrt{2}}{20}
=-6\sqrt{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120\sqrt{2}}{2*10}=\frac{0+120\sqrt{2}}{20}
=\frac{120\sqrt{2}}{20}
=6\sqrt{2}
$