5n^2+n=18

Solution for 5n^2+n=18 equation:

5n^2+n=18

We move all terms to the left:

5n^2+n-(18)=0

a = 5; b = 1; c = -18;
Δ = b2-4ac
Δ = 12-4·5·(-18)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-19}{2*5}=\frac{-20}{10}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+19}{2*5}=\frac{18}{10}
=1+4/5
$