2n^2+n+14=272

Solution for 2n^2+n+14=272 equation:

2n^2+n+14=272

We move all terms to the left:

2n^2+n+14-(272)=0

We add all the numbers together, and all the variables

2n^2+n-258=0

a = 2; b = 1; c = -258;
Δ = b2-4ac
Δ = 12-4·2·(-258)
Δ = 2065
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{2065}}{2*2}=\frac{-1-\sqrt{2065}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{2065}}{2*2}=\frac{-1+\sqrt{2065}}{4}
$