0=4n^2+24n+32

Solution for 0=4n^2+24n+32 equation:

0=4n^2+24n+32

We move all terms to the left:

0-(4n^2+24n+32)=0

We add all the numbers together, and all the variables

-(4n^2+24n+32)=0

We get rid of parentheses

-4n^2-24n-32=0

a = -4; b = -24; c = -32;
Δ = b2-4ac
Δ = -242-4·(-4)·(-32)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8}{2*-4}=\frac{16}{-8}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8}{2*-4}=\frac{32}{-8}
=-4
$