8x=2x^2+2

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

8x=2x^2+2

We move all terms to the left:

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

We get rid of parentheses

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

a = -2; b = 8; c = -2;
Δ = b2-4ac
Δ = 82-4·(-2)·(-2)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{3}}{2*-2}=\frac{-8-4\sqrt{3}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{3}}{2*-2}=\frac{-8+4\sqrt{3}}{-4}
$