8x2+8xN=64

Solution for 8x2+8xN=64 equation:

8x^2+8x=64

We move all terms to the left:

8x^2+8x-(64)=0

a = 8; b = 8; c = -64;
Δ = b2-4ac
Δ = 82-4·8·(-64)
Δ = 2112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2112}=\sqrt{64*33}=\sqrt{64}*\sqrt{33}=8\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{33}}{2*8}=\frac{-8-8\sqrt{33}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{33}}{2*8}=\frac{-8+8\sqrt{33}}{16}
$