6(n+8)n=5

Solution for 6(n+8)n=5 equation:

6(n+8)n=5

We move all terms to the left:

6(n+8)n-(5)=0

We multiply parentheses

6n^2+48n-5=0

a = 6; b = 48; c = -5;
Δ = b2-4ac
Δ = 482-4·6·(-5)
Δ = 2424
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:

$\sqrt{\Delta}=\sqrt{2424}=\sqrt{4*606}=\sqrt{4}*\sqrt{606}=2\sqrt{606}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-2\sqrt{606}}{2*6}=\frac{-48-2\sqrt{606}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+2\sqrt{606}}{2*6}=\frac{-48+2\sqrt{606}}{12}
$