2n^2+4n-14=286

Solution for 2n^2+4n-14=286 equation:

2n^2+4n-14=286

We move all terms to the left:

2n^2+4n-14-(286)=0

We add all the numbers together, and all the variables

2n^2+4n-300=0

a = 2; b = 4; c = -300;
Δ = b2-4ac
Δ = 42-4·2·(-300)
Δ = 2416
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:

$\sqrt{\Delta}=\sqrt{2416}=\sqrt{16*151}=\sqrt{16}*\sqrt{151}=4\sqrt{151}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{151}}{2*2}=\frac{-4-4\sqrt{151}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{151}}{2*2}=\frac{-4+4\sqrt{151}}{4}
$