8n^2+112=-72n

Solution for 8n^2+112=-72n equation:

8n^2+112=-72n

We move all terms to the left:

8n^2+112-(-72n)=0

We get rid of parentheses

8n^2+72n+112=0

a = 8; b = 72; c = +112;
Δ = b2-4ac
Δ = 722-4·8·112
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-40}{2*8}=\frac{-112}{16}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+40}{2*8}=\frac{-32}{16}
=-2
$