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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

2n^2+13n+2=0

a = 2; b = 13; c = +2;
Δ = b2-4ac
Δ = 132-4·2·2
Δ = 153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-3\sqrt{17}}{2*2}=\frac{-13-3\sqrt{17}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+3\sqrt{17}}{2*2}=\frac{-13+3\sqrt{17}}{4}
$