4x^2-592x+20055=0

Solution for 4x^2-592x+20055=0 equation:

4x^2-592x+20055=0

a = 4; b = -592; c = +20055;
Δ = b2-4ac
Δ = -5922-4·4·20055
Δ = 29584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{29584}=172$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-592)-172}{2*4}=\frac{420}{8}
=52+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-592)+172}{2*4}=\frac{764}{8}
=95+1/2
$