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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(V(-2V+12)2), so:

V(-2V+12)2

We multiply parentheses

-4V^2+24V

Back to the equation:

-(-4V^2+24V)


We get rid of parentheses

4V^2-24V+V=0

We add all the numbers together, and all the variables

4V^2-23V=0

a = 4; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·4·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*4}=\frac{0}{8}
=0
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*4}=\frac{46}{8}
=5+3/4
$