81n^2=100

Solution for 81n^2=100 equation:

81n^2=100

We move all terms to the left:

81n^2-(100)=0

a = 81; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·81·(-100)
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-180}{2*81}=\frac{-180}{162}
=-1+1/9
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+180}{2*81}=\frac{180}{162}
=1+1/9
$