4n^2-16n-14=2

Solution for 4n^2-16n-14=2 equation:

4n^2-16n-14=2

We move all terms to the left:

4n^2-16n-14-(2)=0

We add all the numbers together, and all the variables

4n^2-16n-16=0

a = 4; b = -16; c = -16;
Δ = b2-4ac
Δ = -162-4·4·(-16)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16\sqrt{2}}{2*4}=\frac{16-16\sqrt{2}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16\sqrt{2}}{2*4}=\frac{16+16\sqrt{2}}{8}
$