8n(-2n+7)=5

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

8n(-2n+7)=5

We move all terms to the left:

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

We multiply parentheses

-16n^2+56n-5=0

a = -16; b = 56; c = -5;
Δ = b2-4ac
Δ = 562-4·(-16)·(-5)
Δ = 2816
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:

$\sqrt{\Delta}=\sqrt{2816}=\sqrt{256*11}=\sqrt{256}*\sqrt{11}=16\sqrt{11}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-16\sqrt{11}}{2*-16}=\frac{-56-16\sqrt{11}}{-32}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+16\sqrt{11}}{2*-16}=\frac{-56+16\sqrt{11}}{-32}
$