X2-16x+64=20

Solution for X2-16x+64=20 equation:

X2-16X+64=20

We move all terms to the left:

X2-16X+64-(20)=0

We add all the numbers together, and all the variables

X^2-16X+44=0

a = 1; b = -16; c = +44;
Δ = b2-4ac
Δ = -162-4·1·44
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{-(-16)-4\sqrt{5}}{2*1}=\frac{16-4\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{5}}{2*1}=\frac{16+4\sqrt{5}}{2}
$