n(8n+13)=-3

Solution for n(8n+13)=-3 equation:

n(8n+13)=-3

We move all terms to the left:

n(8n+13)-(-3)=0

We add all the numbers together, and all the variables

n(8n+13)+3=0

We multiply parentheses

8n^2+13n+3=0

a = 8; b = 13; c = +3;
Δ = b2-4ac
Δ = 132-4·8·3
Δ = 73
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{73}}{2*8}=\frac{-13-\sqrt{73}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{73}}{2*8}=\frac{-13+\sqrt{73}}{16}
$