X2-20x+50=0

Solution for X2-20x+50=0 equation:

X2-20X+50=0

We add all the numbers together, and all the variables

X^2-20X+50=0

a = 1; b = -20; c = +50;
Δ = b2-4ac
Δ = -202-4·1·50
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10\sqrt{2}}{2*1}=\frac{20-10\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10\sqrt{2}}{2*1}=\frac{20+10\sqrt{2}}{2}
$