11n^2+2n-1=0

Solution for 11n^2+2n-1=0 equation:

11n^2+2n-1=0

a = 11; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·11·(-1)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{3}}{2*11}=\frac{-2-4\sqrt{3}}{22}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{3}}{2*11}=\frac{-2+4\sqrt{3}}{22}
$