10x^2-400x-4000=0

Solution for 10x^2-400x-4000=0 equation:

10x^2-400x-4000=0

a = 10; b = -400; c = -4000;
Δ = b2-4ac
Δ = -4002-4·10·(-4000)
Δ = 320000
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:

$\sqrt{\Delta}=\sqrt{320000}=\sqrt{160000*2}=\sqrt{160000}*\sqrt{2}=400\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-400\sqrt{2}}{2*10}=\frac{400-400\sqrt{2}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+400\sqrt{2}}{2*10}=\frac{400+400\sqrt{2}}{20}
$