1000(2x-200)=(x-1000)*(3x+200)

Solution for 1000(2x-200)=(x-1000)*(3x+200) equation:

1000(2x-200)=(x-1000)(3x+200)

We move all terms to the left:

1000(2x-200)-((x-1000)(3x+200))=0

We multiply parentheses

2000x-((x-1000)(3x+200))-200000=0

We multiply parentheses ..

-((+3x^2+200x-3000x-200000))+2000x-200000=0


We calculate terms in parentheses: -((+3x^2+200x-3000x-200000)), so:

(+3x^2+200x-3000x-200000)

We get rid of parentheses

3x^2+200x-3000x-200000

We add all the numbers together, and all the variables

3x^2-2800x-200000

Back to the equation:

-(3x^2-2800x-200000)


We add all the numbers together, and all the variables

2000x-(3x^2-2800x-200000)-200000=0

We get rid of parentheses

-3x^2+2000x+2800x+200000-200000=0

We add all the numbers together, and all the variables

-3x^2+4800x=0

a = -3; b = 4800; c = 0;
Δ = b2-4ac
Δ = 48002-4·(-3)·0
Δ = 23040000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{23040000}=4800$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4800)-4800}{2*-3}=\frac{-9600}{-6}
=+1600
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4800)+4800}{2*-3}=\frac{0}{-6}
=0
$