3(n+5)n=-8

Solution for 3(n+5)n=-8 equation:

3(n+5)n=-8

We move all terms to the left:

3(n+5)n-(-8)=0

We add all the numbers together, and all the variables

3(n+5)n+8=0

We multiply parentheses

3n^2+15n+8=0

a = 3; b = 15; c = +8;
Δ = b2-4ac
Δ = 152-4·3·8
Δ = 129
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{-(15)-\sqrt{129}}{2*3}=\frac{-15-\sqrt{129}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{129}}{2*3}=\frac{-15+\sqrt{129}}{6}
$