6=14-11n;2

Solution for 6=14-11n;2 equation:

6=14-11n^2

We move all terms to the left:

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

We get rid of parentheses

11n^2-14+6=0

We add all the numbers together, and all the variables

11n^2-8=0

a = 11; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·11·(-8)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{22}}{2*11}=\frac{0-4\sqrt{22}}{22}
=-\frac{4\sqrt{22}}{22}
=-\frac{2\sqrt{22}}{11}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{22}}{2*11}=\frac{0+4\sqrt{22}}{22}
=\frac{4\sqrt{22}}{22}
=\frac{2\sqrt{22}}{11}
$