5000=2x^2+200x

Solution for 5000=2x^2+200x equation:

5000=2x^2+200x

We move all terms to the left:

5000-(2x^2+200x)=0

We get rid of parentheses

-2x^2-200x+5000=0

a = -2; b = -200; c = +5000;
Δ = b2-4ac
Δ = -2002-4·(-2)·5000
Δ = 80000
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:

$\sqrt{\Delta}=\sqrt{80000}=\sqrt{40000*2}=\sqrt{40000}*\sqrt{2}=200\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-200\sqrt{2}}{2*-2}=\frac{200-200\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+200\sqrt{2}}{2*-2}=\frac{200+200\sqrt{2}}{-4}
$