(x^2-64x+128)=0

Solution for (x^2-64x+128)=0 equation:

(x^2-64x+128)=0

We get rid of parentheses

x^2-64x+128=0

a = 1; b = -64; c = +128;
Δ = b2-4ac
Δ = -642-4·1·128
Δ = 3584
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:

$\sqrt{\Delta}=\sqrt{3584}=\sqrt{256*14}=\sqrt{256}*\sqrt{14}=16\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-16\sqrt{14}}{2*1}=\frac{64-16\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+16\sqrt{14}}{2*1}=\frac{64+16\sqrt{14}}{2}
$