5n^2+n=120

Solution for 5n^2+n=120 equation:

5n^2+n=120

We move all terms to the left:

5n^2+n-(120)=0

a = 5; b = 1; c = -120;
Δ = b2-4ac
Δ = 12-4·5·(-120)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-49}{2*5}=\frac{-50}{10}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+49}{2*5}=\frac{48}{10}
=4+4/5
$