11n^2+14n-14=6n

Solution for 11n^2+14n-14=6n equation:

11n^2+14n-14=6n

We move all terms to the left:

11n^2+14n-14-(6n)=0

We add all the numbers together, and all the variables

11n^2+8n-14=0

a = 11; b = 8; c = -14;
Δ = b2-4ac
Δ = 82-4·11·(-14)
Δ = 680
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:

$\sqrt{\Delta}=\sqrt{680}=\sqrt{4*170}=\sqrt{4}*\sqrt{170}=2\sqrt{170}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{170}}{2*11}=\frac{-8-2\sqrt{170}}{22}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{170}}{2*11}=\frac{-8+2\sqrt{170}}{22}
$