x^2-100x+391=0

Solution for x^2-100x+391=0 equation:

x^2-100x+391=0

a = 1; b = -100; c = +391;
Δ = b2-4ac
Δ = -1002-4·1·391
Δ = 8436
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:

$\sqrt{\Delta}=\sqrt{8436}=\sqrt{4*2109}=\sqrt{4}*\sqrt{2109}=2\sqrt{2109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2109}}{2*1}=\frac{100-2\sqrt{2109}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2109}}{2*1}=\frac{100+2\sqrt{2109}}{2}
$