11n^2-2n+2=6

Solution for 11n^2-2n+2=6 equation:

11n^2-2n+2=6

We move all terms to the left:

11n^2-2n+2-(6)=0

We add all the numbers together, and all the variables

11n^2-2n-4=0

a = 11; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·11·(-4)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{5}}{2*11}=\frac{2-6\sqrt{5}}{22}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{5}}{2*11}=\frac{2+6\sqrt{5}}{22}
$