2n^2-n=120

Solution for 2n^2-n=120 equation:

2n^2-n=120

We move all terms to the left:

2n^2-n-(120)=0

We add all the numbers together, and all the variables

2n^2-1n-120=0

a = 2; b = -1; c = -120;
Δ = b2-4ac
Δ = -12-4·2·(-120)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-31}{2*2}=\frac{-30}{4}
=-7+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+31}{2*2}=\frac{32}{4}
=8
$