0=2n^2-n-276

Solution for 0=2n^2-n-276 equation:

0=2n^2-n-276

We move all terms to the left:

0-(2n^2-n-276)=0

We add all the numbers together, and all the variables

-(2n^2-n-276)=0

We get rid of parentheses

-2n^2+n+276=0

a = -2; b = 1; c = +276;
Δ = b2-4ac
Δ = 12-4·(-2)·276
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-47}{2*-2}=\frac{-48}{-4}
=+12
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+47}{2*-2}=\frac{46}{-4}
=-11+1/2
$