n(4n+13)=-4

Solution for n(4n+13)=-4 equation:

n(4n+13)=-4

We move all terms to the left:

n(4n+13)-(-4)=0

We add all the numbers together, and all the variables

n(4n+13)+4=0

We multiply parentheses

4n^2+13n+4=0

a = 4; b = 13; c = +4;
Δ = b2-4ac
Δ = 132-4·4·4
Δ = 105
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{105}}{2*4}=\frac{-13-\sqrt{105}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{105}}{2*4}=\frac{-13+\sqrt{105}}{8}
$