x2-10x-4000=0

Solution for x2-10x-4000=0 equation:

x2-10x-4000=0

We add all the numbers together, and all the variables

x^2-10x-4000=0

a = 1; b = -10; c = -4000;
Δ = b2-4ac
Δ = -102-4·1·(-4000)
Δ = 16100
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:

$\sqrt{\Delta}=\sqrt{16100}=\sqrt{100*161}=\sqrt{100}*\sqrt{161}=10\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{161}}{2*1}=\frac{10-10\sqrt{161}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{161}}{2*1}=\frac{10+10\sqrt{161}}{2}
$