x^2-200x+50=0

Solution for x^2-200x+50=0 equation:

x^2-200x+50=0

a = 1; b = -200; c = +50;
Δ = b2-4ac
Δ = -2002-4·1·50
Δ = 39800
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:

$\sqrt{\Delta}=\sqrt{39800}=\sqrt{100*398}=\sqrt{100}*\sqrt{398}=10\sqrt{398}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-10\sqrt{398}}{2*1}=\frac{200-10\sqrt{398}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+10\sqrt{398}}{2*1}=\frac{200+10\sqrt{398}}{2}
$