x2+40x-8000=0

Solution for x2+40x-8000=0 equation:

x2+40x-8000=0

We add all the numbers together, and all the variables

x^2+40x-8000=0

a = 1; b = 40; c = -8000;
Δ = b2-4ac
Δ = 402-4·1·(-8000)
Δ = 33600
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:

$\sqrt{\Delta}=\sqrt{33600}=\sqrt{1600*21}=\sqrt{1600}*\sqrt{21}=40\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40\sqrt{21}}{2*1}=\frac{-40-40\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40\sqrt{21}}{2*1}=\frac{-40+40\sqrt{21}}{2}
$