8n(4n+7)=1

Solution for 8n(4n+7)=1 equation:

8n(4n+7)=1

We move all terms to the left:

8n(4n+7)-(1)=0

We multiply parentheses

32n^2+56n-1=0

a = 32; b = 56; c = -1;
Δ = b2-4ac
Δ = 562-4·32·(-1)
Δ = 3264
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:

$\sqrt{\Delta}=\sqrt{3264}=\sqrt{64*51}=\sqrt{64}*\sqrt{51}=8\sqrt{51}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-8\sqrt{51}}{2*32}=\frac{-56-8\sqrt{51}}{64}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+8\sqrt{51}}{2*32}=\frac{-56+8\sqrt{51}}{64}
$