8n^2=24n+80

Solution for 8n^2=24n+80 equation:

8n^2=24n+80

We move all terms to the left:

8n^2-(24n+80)=0

We get rid of parentheses

8n^2-24n-80=0

a = 8; b = -24; c = -80;
Δ = b2-4ac
Δ = -242-4·8·(-80)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-56}{2*8}=\frac{-32}{16}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+56}{2*8}=\frac{80}{16}
=5
$