V=(200-2x)(150-2x)

Solution for V=(200-2x)(150-2x) equation:

=(200-2V)(150-2V)

We move all terms to the left:

-((200-2V)(150-2V))=0

We add all the numbers together, and all the variables

-((-2V+200)(-2V+150))=0

We multiply parentheses ..

-((+4V^2-300V-400V+30000))=0


We calculate terms in parentheses: -((+4V^2-300V-400V+30000)), so:

(+4V^2-300V-400V+30000)

We get rid of parentheses

4V^2-300V-400V+30000

We add all the numbers together, and all the variables

4V^2-700V+30000

Back to the equation:

-(4V^2-700V+30000)


We get rid of parentheses

-4V^2+700V-30000=0

a = -4; b = 700; c = -30000;
Δ = b2-4ac
Δ = 7002-4·(-4)·(-30000)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(700)-100}{2*-4}=\frac{-800}{-8}
=+100
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(700)+100}{2*-4}=\frac{-600}{-8}
=+75
$