4x^2-640X+6400=0

Solution for 4x^2-640X+6400=0 equation:

4x^2-640x+6400=0

a = 4; b = -640; c = +6400;
Δ = b2-4ac
Δ = -6402-4·4·6400
Δ = 307200
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:

$\sqrt{\Delta}=\sqrt{307200}=\sqrt{102400*3}=\sqrt{102400}*\sqrt{3}=320\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-640)-320\sqrt{3}}{2*4}=\frac{640-320\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-640)+320\sqrt{3}}{2*4}=\frac{640+320\sqrt{3}}{8}
$