V(x)=(18-2x)(3-2x)

Solution for V(x)=(18-2x)(3-2x) equation:

(V)=(18-2V)(3-2V)

We move all terms to the left:

(V)-((18-2V)(3-2V))=0

We add all the numbers together, and all the variables

V-((-2V+18)(-2V+3))=0

We multiply parentheses ..

-((+4V^2-6V-36V+54))+V=0


We calculate terms in parentheses: -((+4V^2-6V-36V+54)), so:

(+4V^2-6V-36V+54)

We get rid of parentheses

4V^2-6V-36V+54

We add all the numbers together, and all the variables

4V^2-42V+54

Back to the equation:

-(4V^2-42V+54)


We add all the numbers together, and all the variables

V-(4V^2-42V+54)=0

We get rid of parentheses

-4V^2+V+42V-54=0

We add all the numbers together, and all the variables

-4V^2+43V-54=0

a = -4; b = 43; c = -54;
Δ = b2-4ac
Δ = 432-4·(-4)·(-54)
Δ = 985
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{-(43)-\sqrt{985}}{2*-4}=\frac{-43-\sqrt{985}}{-8}
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+\sqrt{985}}{2*-4}=\frac{-43+\sqrt{985}}{-8}
$