V(x)=(24-2x)(18-2x)

Solution for V(x)=(24-2x)(18-2x) equation:

(V)=(24-2V)(18-2V)

We move all terms to the left:

(V)-((24-2V)(18-2V))=0

We add all the numbers together, and all the variables

V-((-2V+24)(-2V+18))=0

We multiply parentheses ..

-((+4V^2-36V-48V+432))+V=0


We calculate terms in parentheses: -((+4V^2-36V-48V+432)), so:

(+4V^2-36V-48V+432)

We get rid of parentheses

4V^2-36V-48V+432

We add all the numbers together, and all the variables

4V^2-84V+432

Back to the equation:

-(4V^2-84V+432)


We add all the numbers together, and all the variables

V-(4V^2-84V+432)=0

We get rid of parentheses

-4V^2+V+84V-432=0

We add all the numbers together, and all the variables

-4V^2+85V-432=0

a = -4; b = 85; c = -432;
Δ = b2-4ac
Δ = 852-4·(-4)·(-432)
Δ = 313
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(85)-\sqrt{313}}{2*-4}=\frac{-85-\sqrt{313}}{-8}
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+\sqrt{313}}{2*-4}=\frac{-85+\sqrt{313}}{-8}
$