x^2+4x=10000

Solution for x^2+4x=10000 equation:

x^2+4x=10000

We move all terms to the left:

x^2+4x-(10000)=0

a = 1; b = 4; c = -10000;
Δ = b2-4ac
Δ = 42-4·1·(-10000)
Δ = 40016
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:

$\sqrt{\Delta}=\sqrt{40016}=\sqrt{16*2501}=\sqrt{16}*\sqrt{2501}=4\sqrt{2501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2501}}{2*1}=\frac{-4-4\sqrt{2501}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2501}}{2*1}=\frac{-4+4\sqrt{2501}}{2}
$