8n(6n+5)=5

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

8n(6n+5)=5

We move all terms to the left:

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

We multiply parentheses

48n^2+40n-5=0

a = 48; b = 40; c = -5;
Δ = b2-4ac
Δ = 402-4·48·(-5)
Δ = 2560
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:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-16\sqrt{10}}{2*48}=\frac{-40-16\sqrt{10}}{96}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+16\sqrt{10}}{2*48}=\frac{-40+16\sqrt{10}}{96}
$