2n^2=24-8n

Solution for 2n^2=24-8n equation:

2n^2=24-8n

We move all terms to the left:

2n^2-(24-8n)=0

We add all the numbers together, and all the variables

2n^2-(-8n+24)=0

We get rid of parentheses

2n^2+8n-24=0

a = 2; b = 8; c = -24;
Δ = b2-4ac
Δ = 82-4·2·(-24)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16}{2*2}=\frac{-24}{4}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16}{2*2}=\frac{8}{4}
=2
$