x2-100x+800=0

Solution for x2-100x+800=0 equation:

x2-100x+800=0

We add all the numbers together, and all the variables

x^2-100x+800=0

a = 1; b = -100; c = +800;
Δ = b2-4ac
Δ = -1002-4·1·800
Δ = 6800
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:

$\sqrt{\Delta}=\sqrt{6800}=\sqrt{400*17}=\sqrt{400}*\sqrt{17}=20\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{17}}{2*1}=\frac{100-20\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{17}}{2*1}=\frac{100+20\sqrt{17}}{2}
$