x^2-256x+2304=0

Solution for x^2-256x+2304=0 equation:

x^2-256x+2304=0

a = 1; b = -256; c = +2304;
Δ = b2-4ac
Δ = -2562-4·1·2304
Δ = 56320
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:

$\sqrt{\Delta}=\sqrt{56320}=\sqrt{1024*55}=\sqrt{1024}*\sqrt{55}=32\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-256)-32\sqrt{55}}{2*1}=\frac{256-32\sqrt{55}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-256)+32\sqrt{55}}{2*1}=\frac{256+32\sqrt{55}}{2}
$