3n^2-100*n+100=0

Solution for 3n^2-100*n+100=0 equation:

3n^2-100n+100=0

a = 3; b = -100; c = +100;
Δ = b2-4ac
Δ = -1002-4·3·100
Δ = 8800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8800}=\sqrt{400*22}=\sqrt{400}*\sqrt{22}=20\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{22}}{2*3}=\frac{100-20\sqrt{22}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{22}}{2*3}=\frac{100+20\sqrt{22}}{6}
$