x2-20x-400=0

Solution for x2-20x-400=0 equation:

x2-20x-400=0

We add all the numbers together, and all the variables

x^2-20x-400=0

a = 1; b = -20; c = -400;
Δ = b2-4ac
Δ = -202-4·1·(-400)
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{5}}{2*1}=\frac{20-20\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{5}}{2*1}=\frac{20+20\sqrt{5}}{2}
$