50x^2-664x+2114=0

Solution for 50x^2-664x+2114=0 equation:

50x^2-664x+2114=0

a = 50; b = -664; c = +2114;
Δ = b2-4ac
Δ = -6642-4·50·2114
Δ = 18096
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:

$\sqrt{\Delta}=\sqrt{18096}=\sqrt{16*1131}=\sqrt{16}*\sqrt{1131}=4\sqrt{1131}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-664)-4\sqrt{1131}}{2*50}=\frac{664-4\sqrt{1131}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-664)+4\sqrt{1131}}{2*50}=\frac{664+4\sqrt{1131}}{100}
$