x^2+10x=5000

Solution for x^2+10x=5000 equation:

x^2+10x=5000

We move all terms to the left:

x^2+10x-(5000)=0

a = 1; b = 10; c = -5000;
Δ = b2-4ac
Δ = 102-4·1·(-5000)
Δ = 20100
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:

$\sqrt{\Delta}=\sqrt{20100}=\sqrt{100*201}=\sqrt{100}*\sqrt{201}=10\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{201}}{2*1}=\frac{-10-10\sqrt{201}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{201}}{2*1}=\frac{-10+10\sqrt{201}}{2}
$