x2-10x-400=0

Solution for x2-10x-400=0 equation:

x2-10x-400=0

We add all the numbers together, and all the variables

x^2-10x-400=0

a = 1; b = -10; c = -400;
Δ = b2-4ac
Δ = -102-4·1·(-400)
Δ = 1700
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:

$\sqrt{\Delta}=\sqrt{1700}=\sqrt{100*17}=\sqrt{100}*\sqrt{17}=10\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{17}}{2*1}=\frac{10-10\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{17}}{2*1}=\frac{10+10\sqrt{17}}{2}
$