11n2=-1+7n

Solution for 11n2=-1+7n equation:

11n^2=-1+7n

We move all terms to the left:

11n^2-(-1+7n)=0

We add all the numbers together, and all the variables

11n^2-(7n-1)=0

We get rid of parentheses

11n^2-7n+1=0

a = 11; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·11·1
Δ = 5
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{5}}{2*11}=\frac{7-\sqrt{5}}{22}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{5}}{2*11}=\frac{7+\sqrt{5}}{22}
$