V(a)=(8-2a)(6a-2a)

Solution for V(a)=(8-2a)(6a-2a) equation:

(V)=(8-2V)(6V-2V)

We move all terms to the left:

(V)-((8-2V)(6V-2V))=0

We add all the numbers together, and all the variables

V-((-2V+8)(+4V))=0

We multiply parentheses ..

-((-8V^2+32V))+V=0


We calculate terms in parentheses: -((-8V^2+32V)), so:

(-8V^2+32V)

We get rid of parentheses

-8V^2+32V

Back to the equation:

-(-8V^2+32V)


We get rid of parentheses

8V^2-32V+V=0

We add all the numbers together, and all the variables

8V^2-31V=0

a = 8; b = -31; c = 0;
Δ = b2-4ac
Δ = -312-4·8·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-31}{2*8}=\frac{0}{16}
=0
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+31}{2*8}=\frac{62}{16}
=3+7/8
$