8n(3n+4)=31

Solution for 8n(3n+4)=31 equation:

8n(3n+4)=31

We move all terms to the left:

8n(3n+4)-(31)=0

We multiply parentheses

24n^2+32n-31=0

a = 24; b = 32; c = -31;
Δ = b2-4ac
Δ = 322-4·24·(-31)
Δ = 4000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-20\sqrt{10}}{2*24}=\frac{-32-20\sqrt{10}}{48}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+20\sqrt{10}}{2*24}=\frac{-32+20\sqrt{10}}{48}
$