V=(500-2x)X-1000+100x

Solution for V=(500-2x)X-1000+100x equation:

=(500-2V)V-1000+100V

We move all terms to the left:

-((500-2V)V-1000+100V)=0

We add all the numbers together, and all the variables

-((-2V+500)V-1000+100V)=0


We calculate terms in parentheses: -((-2V+500)V-1000+100V), so:

(-2V+500)V-1000+100V

determiningTheFunctionDomain
(-2V+500)V+100V-1000

We add all the numbers together, and all the variables

100V+(-2V+500)V-1000

We multiply parentheses

-2V^2+100V+500V-1000

We add all the numbers together, and all the variables

-2V^2+600V-1000

Back to the equation:

-(-2V^2+600V-1000)


We get rid of parentheses

2V^2-600V+1000=0

a = 2; b = -600; c = +1000;
Δ = b2-4ac
Δ = -6002-4·2·1000
Δ = 352000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{352000}=\sqrt{6400*55}=\sqrt{6400}*\sqrt{55}=80\sqrt{55}$
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-80\sqrt{55}}{2*2}=\frac{600-80\sqrt{55}}{4}
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+80\sqrt{55}}{2*2}=\frac{600+80\sqrt{55}}{4}
$