10n^2-9=81

Solution for 10n^2-9=81 equation:

10n^2-9=81

We move all terms to the left:

10n^2-9-(81)=0

We add all the numbers together, and all the variables

10n^2-90=0

a = 10; b = 0; c = -90;
Δ = b2-4ac
Δ = 02-4·10·(-90)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60}{2*10}=\frac{-60}{20}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60}{2*10}=\frac{60}{20}
=3
$