20000-200x+x^2=20000-400x+3x^2

Solution for 20000-200x+x^2=20000-400x+3x^2 equation:

20000-200x+x^2=20000-400x+3x^2

We move all terms to the left:

20000-200x+x^2-(20000-400x+3x^2)=0

We get rid of parentheses

x^2-3x^2+400x-200x-20000+20000=0

We add all the numbers together, and all the variables

-2x^2+200x=0

a = -2; b = 200; c = 0;
Δ = b2-4ac
Δ = 2002-4·(-2)·0
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-200}{2*-2}=\frac{-400}{-4}
=+100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+200}{2*-2}=\frac{0}{-4}
=0
$