3200=(200-x)x-(2800+45x)

Solution for 3200=(200-x)x-(2800+45x) equation:

3200=(200-x)x-(2800+45x)

We move all terms to the left:

3200-((200-x)x-(2800+45x))=0

We add all the numbers together, and all the variables

-((-1x+200)x-(45x+2800))+3200=0


We calculate terms in parentheses: -((-1x+200)x-(45x+2800)), so:

(-1x+200)x-(45x+2800)

We multiply parentheses

-1x^2+200x-(45x+2800)

We get rid of parentheses

-1x^2+200x-45x-2800

We add all the numbers together, and all the variables

-1x^2+155x-2800

Back to the equation:

-(-1x^2+155x-2800)


We get rid of parentheses

1x^2-155x+2800+3200=0

We add all the numbers together, and all the variables

x^2-155x+6000=0

a = 1; b = -155; c = +6000;
Δ = b2-4ac
Δ = -1552-4·1·6000
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-155)-5}{2*1}=\frac{150}{2}
=75
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-155)+5}{2*1}=\frac{160}{2}
=80
$