2n^2+n=240

Solution for 2n^2+n=240 equation:

2n^2+n=240

We move all terms to the left:

2n^2+n-(240)=0

a = 2; b = 1; c = -240;
Δ = b2-4ac
Δ = 12-4·2·(-240)
Δ = 1921
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{1921}}{2*2}=\frac{-1-\sqrt{1921}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1921}}{2*2}=\frac{-1+\sqrt{1921}}{4}
$