8-2x=8x^2

Solution for 8-2x=8x^2 equation:

8-2x=8x^2

We move all terms to the left:

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

determiningTheFunctionDomain
-8x^2-2x+8=0

a = -8; b = -2; c = +8;
Δ = b2-4ac
Δ = -22-4·(-8)·8
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{65}}{2*-8}=\frac{2-2\sqrt{65}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{65}}{2*-8}=\frac{2+2\sqrt{65}}{-16}
$