X2+400x-4000=0

Solution for X2+400x-4000=0 equation:

X2+400X-4000=0

We add all the numbers together, and all the variables

X^2+400X-4000=0

a = 1; b = 400; c = -4000;
Δ = b2-4ac
Δ = 4002-4·1·(-4000)
Δ = 176000
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:

$\sqrt{\Delta}=\sqrt{176000}=\sqrt{1600*110}=\sqrt{1600}*\sqrt{110}=40\sqrt{110}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-40\sqrt{110}}{2*1}=\frac{-400-40\sqrt{110}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+40\sqrt{110}}{2*1}=\frac{-400+40\sqrt{110}}{2}
$