2x^2-500x=20,000

Solution for 2x^2-500x=20,000 equation:

2x^2-500x=20.000

We move all terms to the left:

2x^2-500x-(20.000)=0

We add all the numbers together, and all the variables

2x^2-500x-20=0

a = 2; b = -500; c = -20;
Δ = b2-4ac
Δ = -5002-4·2·(-20)
Δ = 250160
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:

$\sqrt{\Delta}=\sqrt{250160}=\sqrt{16*15635}=\sqrt{16}*\sqrt{15635}=4\sqrt{15635}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-4\sqrt{15635}}{2*2}=\frac{500-4\sqrt{15635}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+4\sqrt{15635}}{2*2}=\frac{500+4\sqrt{15635}}{4}
$