x^2-334x+119=0

Solution for x^2-334x+119=0 equation:

x^2-334x+119=0

a = 1; b = -334; c = +119;
Δ = b2-4ac
Δ = -3342-4·1·119
Δ = 111080
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:

$\sqrt{\Delta}=\sqrt{111080}=\sqrt{4*27770}=\sqrt{4}*\sqrt{27770}=2\sqrt{27770}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-334)-2\sqrt{27770}}{2*1}=\frac{334-2\sqrt{27770}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-334)+2\sqrt{27770}}{2*1}=\frac{334+2\sqrt{27770}}{2}
$