8n(2n+5)=31

Solution for 8n(2n+5)=31 equation:

8n(2n+5)=31

We move all terms to the left:

8n(2n+5)-(31)=0

We multiply parentheses

16n^2+40n-31=0

a = 16; b = 40; c = -31;
Δ = b2-4ac
Δ = 402-4·16·(-31)
Δ = 3584
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:

$\sqrt{\Delta}=\sqrt{3584}=\sqrt{256*14}=\sqrt{256}*\sqrt{14}=16\sqrt{14}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-16\sqrt{14}}{2*16}=\frac{-40-16\sqrt{14}}{32}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+16\sqrt{14}}{2*16}=\frac{-40+16\sqrt{14}}{32}
$