x^2=-8x+4

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

x^2=-8x+4

We move all terms to the left:

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

We get rid of parentheses

x^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}
$