n^2-7=81

Solution for n^2-7=81 equation:

n^2-7=81

We move all terms to the left:

n^2-7-(81)=0

We add all the numbers together, and all the variables

n^2-88=0

a = 1; b = 0; c = -88;
Δ = b2-4ac
Δ = 02-4·1·(-88)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{22}}{2*1}=\frac{0-4\sqrt{22}}{2}
=-\frac{4\sqrt{22}}{2}
=-2\sqrt{22}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{22}}{2*1}=\frac{0+4\sqrt{22}}{2}
=\frac{4\sqrt{22}}{2}
=2\sqrt{22}
$