x^2+100x=2000

Solution for x^2+100x=2000 equation:

x^2+100x=2000

We move all terms to the left:

x^2+100x-(2000)=0

a = 1; b = 100; c = -2000;
Δ = b2-4ac
Δ = 1002-4·1·(-2000)
Δ = 18000
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:

$\sqrt{\Delta}=\sqrt{18000}=\sqrt{3600*5}=\sqrt{3600}*\sqrt{5}=60\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-60\sqrt{5}}{2*1}=\frac{-100-60\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+60\sqrt{5}}{2*1}=\frac{-100+60\sqrt{5}}{2}
$