u^2-50u+100=0

Solution for u^2-50u+100=0 equation:

u^2-50u+100=0

a = 1; b = -50; c = +100;
Δ = b2-4ac
Δ = -502-4·1·100
Δ = 2100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{21}}{2*1}=\frac{50-10\sqrt{21}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{21}}{2*1}=\frac{50+10\sqrt{21}}{2}
$