8n(6n+1)=392

Solution for 8n(6n+1)=392 equation:

8n(6n+1)=392

We move all terms to the left:

8n(6n+1)-(392)=0

We multiply parentheses

48n^2+8n-392=0

a = 48; b = 8; c = -392;
Δ = b2-4ac
Δ = 82-4·48·(-392)
Δ = 75328
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:

$\sqrt{\Delta}=\sqrt{75328}=\sqrt{64*1177}=\sqrt{64}*\sqrt{1177}=8\sqrt{1177}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{1177}}{2*48}=\frac{-8-8\sqrt{1177}}{96}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{1177}}{2*48}=\frac{-8+8\sqrt{1177}}{96}
$