X^2-8x+16=-14+64

Solution for X^2-8x+16=-14+64 equation:

X^2-8X+16=-14+64

We move all terms to the left:

X^2-8X+16-(-14+64)=0

We add all the numbers together, and all the variables

X^2-8X+16-50=0

We add all the numbers together, and all the variables

X^2-8X-34=0

a = 1; b = -8; c = -34;
Δ = b2-4ac
Δ = -82-4·1·(-34)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-10\sqrt{2}}{2*1}=\frac{8-10\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+10\sqrt{2}}{2*1}=\frac{8+10\sqrt{2}}{2}
$