91=9n^2+10

Solution for 91=9n^2+10 equation:

91=9n^2+10

We move all terms to the left:

91-(9n^2+10)=0

We get rid of parentheses

-9n^2-10+91=0

We add all the numbers together, and all the variables

-9n^2+81=0

a = -9; b = 0; c = +81;
Δ = b2-4ac
Δ = 02-4·(-9)·81
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54}{2*-9}=\frac{-54}{-18}
=+3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54}{2*-9}=\frac{54}{-18}
=-3
$