300x-2x^2=100x+2000

Solution for 300x-2x^2=100x+2000 equation:

300x-2x^2=100x+2000

We move all terms to the left:

300x-2x^2-(100x+2000)=0

We get rid of parentheses

-2x^2+300x-100x-2000=0

We add all the numbers together, and all the variables

-2x^2+200x-2000=0

a = -2; b = 200; c = -2000;
Δ = b2-4ac
Δ = 2002-4·(-2)·(-2000)
Δ = 24000
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:

$\sqrt{\Delta}=\sqrt{24000}=\sqrt{1600*15}=\sqrt{1600}*\sqrt{15}=40\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-40\sqrt{15}}{2*-2}=\frac{-200-40\sqrt{15}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+40\sqrt{15}}{2*-2}=\frac{-200+40\sqrt{15}}{-4}
$