100x^2-40x+1=0

Solution for 100x^2-40x+1=0 equation:

100x^2-40x+1=0

a = 100; b = -40; c = +1;
Δ = b2-4ac
Δ = -402-4·100·1
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-20\sqrt{3}}{2*100}=\frac{40-20\sqrt{3}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+20\sqrt{3}}{2*100}=\frac{40+20\sqrt{3}}{200}
$