10^2-n^2-16=0

Solution for 10^2-n^2-16=0 equation:

10^2-n^2-16=0

We add all the numbers together, and all the variables

-1n^2+84=0

a = -1; b = 0; c = +84;
Δ = b2-4ac
Δ = 02-4·(-1)·84
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{21}}{2*-1}=\frac{0-4\sqrt{21}}{-2}
=-\frac{4\sqrt{21}}{-2}
=-\frac{2\sqrt{21}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{21}}{2*-1}=\frac{0+4\sqrt{21}}{-2}
=\frac{4\sqrt{21}}{-2}
=\frac{2\sqrt{21}}{-1}
$