10n^2-10=410

Solution for 10n^2-10=410 equation:

10n^2-10=410

We move all terms to the left:

10n^2-10-(410)=0

We add all the numbers together, and all the variables

10n^2-420=0

a = 10; b = 0; c = -420;
Δ = b2-4ac
Δ = 02-4·10·(-420)
Δ = 16800
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:

$\sqrt{\Delta}=\sqrt{16800}=\sqrt{400*42}=\sqrt{400}*\sqrt{42}=20\sqrt{42}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{42}}{2*10}=\frac{0-20\sqrt{42}}{20}
=-\frac{20\sqrt{42}}{20}
=-\sqrt{42}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{42}}{2*10}=\frac{0+20\sqrt{42}}{20}
=\frac{20\sqrt{42}}{20}
=\sqrt{42}
$