4=x^2+8x

Solution for 4=x^2+8x equation:

4=x^2+8x

We move all terms to the left:

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

We get rid of parentheses

-x^2-8x+4=0

We add all the numbers together, and all the variables

-1x^2-8x+4=0

a = -1; b = -8; c = +4;
Δ = b2-4ac
Δ = -82-4·(-1)·4
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{5}}{2*-1}=\frac{8-4\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{5}}{2*-1}=\frac{8+4\sqrt{5}}{-2}
$