17n^2=n^2+8^2

Solution for 17n^2=n^2+8^2 equation:

17n^2=n^2+8^2

We move all terms to the left:

17n^2-(n^2+8^2)=0

We get rid of parentheses

17n^2-n^2-8^2=0

We add all the numbers together, and all the variables

16n^2-64=0

a = 16; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·16·(-64)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64}{2*16}=\frac{-64}{32}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64}{2*16}=\frac{64}{32}
=2
$