10n^2-1=879

Solution for 10n^2-1=879 equation:

10n^2-1=879

We move all terms to the left:

10n^2-1-(879)=0

We add all the numbers together, and all the variables

10n^2-880=0

a = 10; b = 0; c = -880;
Δ = b2-4ac
Δ = 02-4·10·(-880)
Δ = 35200
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:

$\sqrt{\Delta}=\sqrt{35200}=\sqrt{1600*22}=\sqrt{1600}*\sqrt{22}=40\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{22}}{2*10}=\frac{0-40\sqrt{22}}{20}
=-\frac{40\sqrt{22}}{20}
=-2\sqrt{22}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{22}}{2*10}=\frac{0+40\sqrt{22}}{20}
=\frac{40\sqrt{22}}{20}
=2\sqrt{22}
$