8n(6n+7)=1

Solution for 8n(6n+7)=1 equation:

8n(6n+7)=1

We move all terms to the left:

8n(6n+7)-(1)=0

We multiply parentheses

48n^2+56n-1=0

a = 48; b = 56; c = -1;
Δ = b2-4ac
Δ = 562-4·48·(-1)
Δ = 3328
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:

$\sqrt{\Delta}=\sqrt{3328}=\sqrt{256*13}=\sqrt{256}*\sqrt{13}=16\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-16\sqrt{13}}{2*48}=\frac{-56-16\sqrt{13}}{96}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+16\sqrt{13}}{2*48}=\frac{-56+16\sqrt{13}}{96}
$