X^2-8x+16=52

Solution for X^2-8x+16=52 equation:

X^2-8X+16=52

We move all terms to the left:

X^2-8X+16-(52)=0

We add all the numbers together, and all the variables

X^2-8X-36=0

a = 1; b = -8; c = -36;
Δ = b2-4ac
Δ = -82-4·1·(-36)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{13}}{2*1}=\frac{8-4\sqrt{13}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{13}}{2*1}=\frac{8+4\sqrt{13}}{2}
$