4x^2-255x+2200=0

Solution for 4x^2-255x+2200=0 equation:

4x^2-255x+2200=0

a = 4; b = -255; c = +2200;
Δ = b2-4ac
Δ = -2552-4·4·2200
Δ = 29825
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:

$\sqrt{\Delta}=\sqrt{29825}=\sqrt{25*1193}=\sqrt{25}*\sqrt{1193}=5\sqrt{1193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-255)-5\sqrt{1193}}{2*4}=\frac{255-5\sqrt{1193}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-255)+5\sqrt{1193}}{2*4}=\frac{255+5\sqrt{1193}}{8}
$