x2+40x-8000=9

Solution for x2+40x-8000=9 equation:

x2+40x-8000=9

We move all terms to the left:

x2+40x-8000-(9)=0

We add all the numbers together, and all the variables

x^2+40x-8009=0

a = 1; b = 40; c = -8009;
Δ = b2-4ac
Δ = 402-4·1·(-8009)
Δ = 33636
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:

$\sqrt{\Delta}=\sqrt{33636}=\sqrt{4*8409}=\sqrt{4}*\sqrt{8409}=2\sqrt{8409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{8409}}{2*1}=\frac{-40-2\sqrt{8409}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{8409}}{2*1}=\frac{-40+2\sqrt{8409}}{2}
$