x^2+11x-4000=0

Solution for x^2+11x-4000=0 equation:

x^2+11x-4000=0

a = 1; b = 11; c = -4000;
Δ = b2-4ac
Δ = 112-4·1·(-4000)
Δ = 16121
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:

$\sqrt{\Delta}=\sqrt{16121}=\sqrt{49*329}=\sqrt{49}*\sqrt{329}=7\sqrt{329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-7\sqrt{329}}{2*1}=\frac{-11-7\sqrt{329}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+7\sqrt{329}}{2*1}=\frac{-11+7\sqrt{329}}{2}
$