n^2+16=10n^2

Solution for n^2+16=10n^2 equation:

n^2+16=10n^2

We move all terms to the left:

n^2+16-(10n^2)=0

We add all the numbers together, and all the variables

-9n^2+16=0

a = -9; b = 0; c = +16;
Δ = b2-4ac
Δ = 02-4·(-9)·16
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*-9}=\frac{-24}{-18}
=1+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*-9}=\frac{24}{-18}
=-1+1/3
$