x^2-192x+1024=0

Solution for x^2-192x+1024=0 equation:

x^2-192x+1024=0

a = 1; b = -192; c = +1024;
Δ = b2-4ac
Δ = -1922-4·1·1024
Δ = 32768
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:

$\sqrt{\Delta}=\sqrt{32768}=\sqrt{16384*2}=\sqrt{16384}*\sqrt{2}=128\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-128\sqrt{2}}{2*1}=\frac{192-128\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+128\sqrt{2}}{2*1}=\frac{192+128\sqrt{2}}{2}
$