8n(5n+7)=2

Solution for 8n(5n+7)=2 equation:

8n(5n+7)=2

We move all terms to the left:

8n(5n+7)-(2)=0

We multiply parentheses

40n^2+56n-2=0

a = 40; b = 56; c = -2;
Δ = b2-4ac
Δ = 562-4·40·(-2)
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-24\sqrt{6}}{2*40}=\frac{-56-24\sqrt{6}}{80}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+24\sqrt{6}}{2*40}=\frac{-56+24\sqrt{6}}{80}
$