8n(5n+7)=8

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

8n(5n+7)=8

We move all terms to the left:

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

We multiply parentheses

40n^2+56n-8=0

a = 40; b = 56; c = -8;
Δ = b2-4ac
Δ = 562-4·40·(-8)
Δ = 4416
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:

$\sqrt{\Delta}=\sqrt{4416}=\sqrt{64*69}=\sqrt{64}*\sqrt{69}=8\sqrt{69}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-8\sqrt{69}}{2*40}=\frac{-56-8\sqrt{69}}{80}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+8\sqrt{69}}{2*40}=\frac{-56+8\sqrt{69}}{80}
$