V=((24-2x)(12-2x))

Solution for V=((24-2x)(12-2x)) equation:

=((24-2V)(12-2V))

We move all terms to the left:

-(((24-2V)(12-2V)))=0

We add all the numbers together, and all the variables

-(((-2V+24)(-2V+12)))=0

We multiply parentheses ..

-(((+4V^2-24V-48V+288)))=0


We calculate terms in parentheses: -(((+4V^2-24V-48V+288))), so:

((+4V^2-24V-48V+288))


We calculate terms in parentheses: +((+4V^2-24V-48V+288)), so:

(+4V^2-24V-48V+288)

We get rid of parentheses

4V^2-24V-48V+288

We add all the numbers together, and all the variables

4V^2-72V+288

Back to the equation:

+(4V^2-72V+288)


We get rid of parentheses

4V^2-72V+288

Back to the equation:

-(4V^2-72V+288)


We get rid of parentheses

-4V^2+72V-288=0

a = -4; b = 72; c = -288;
Δ = b2-4ac
Δ = 722-4·(-4)·(-288)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-24}{2*-4}=\frac{-96}{-8}
=+12
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+24}{2*-4}=\frac{-48}{-8}
=+6
$