x*x+2000x=5000

Solution for x*x+2000x=5000 equation:

x*x+2000x=5000

We move all terms to the left:

x*x+2000x-(5000)=0

We add all the numbers together, and all the variables

2000x+x*x-5000=0

Wy multiply elements

x^2+2000x-5000=0

a = 1; b = 2000; c = -5000;
Δ = b2-4ac
Δ = 20002-4·1·(-5000)
Δ = 4020000
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:

$\sqrt{\Delta}=\sqrt{4020000}=\sqrt{10000*402}=\sqrt{10000}*\sqrt{402}=100\sqrt{402}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2000)-100\sqrt{402}}{2*1}=\frac{-2000-100\sqrt{402}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2000)+100\sqrt{402}}{2*1}=\frac{-2000+100\sqrt{402}}{2}
$