8n^2=320-24n

Solution for 8n^2=320-24n equation:

8n^2=320-24n

We move all terms to the left:

8n^2-(320-24n)=0

We add all the numbers together, and all the variables

8n^2-(-24n+320)=0

We get rid of parentheses

8n^2+24n-320=0

a = 8; b = 24; c = -320;
Δ = b2-4ac
Δ = 242-4·8·(-320)
Δ = 10816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10816}=104$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-104}{2*8}=\frac{-128}{16}
=-8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+104}{2*8}=\frac{80}{16}
=5
$