n2+10n2+10=91

Solution for n2+10n2+10=91 equation:

n2+10n^2+10=91

We move all terms to the left:

n2+10n^2+10-(91)=0

We add all the numbers together, and all the variables

11n^2-81=0

a = 11; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·11·(-81)
Δ = 3564
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:

$\sqrt{\Delta}=\sqrt{3564}=\sqrt{324*11}=\sqrt{324}*\sqrt{11}=18\sqrt{11}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{11}}{2*11}=\frac{0-18\sqrt{11}}{22}
=-\frac{18\sqrt{11}}{22}
=-\frac{9\sqrt{11}}{11}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{11}}{2*11}=\frac{0+18\sqrt{11}}{22}
=\frac{18\sqrt{11}}{22}
=\frac{9\sqrt{11}}{11}
$