2000=100x+5x^2

Solution for 2000=100x+5x^2 equation:

2000=100x+5x^2

We move all terms to the left:

2000-(100x+5x^2)=0

We get rid of parentheses

-5x^2-100x+2000=0

a = -5; b = -100; c = +2000;
Δ = b2-4ac
Δ = -1002-4·(-5)·2000
Δ = 50000
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:

$\sqrt{\Delta}=\sqrt{50000}=\sqrt{10000*5}=\sqrt{10000}*\sqrt{5}=100\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-100\sqrt{5}}{2*-5}=\frac{100-100\sqrt{5}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+100\sqrt{5}}{2*-5}=\frac{100+100\sqrt{5}}{-10}
$