2n^2+13n+18=-1

Solution for 2n^2+13n+18=-1 equation:

2n^2+13n+18=-1

We move all terms to the left:

2n^2+13n+18-(-1)=0

We add all the numbers together, and all the variables

2n^2+13n+19=0

a = 2; b = 13; c = +19;
Δ = b2-4ac
Δ = 132-4·2·19
Δ = 17
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{-(13)-\sqrt{17}}{2*2}=\frac{-13-\sqrt{17}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{17}}{2*2}=\frac{-13+\sqrt{17}}{4}
$