V(x)=(4-2)(10-2x)(x)

Solution for V(x)=(4-2)(10-2x)(x) equation:

(V)=(4-2)(10-2V)(V)

We move all terms to the left:

(V)-((4-2)(10-2V)(V))=0

We add all the numbers together, and all the variables

V-(2(-2V+10)V)=0


We calculate terms in parentheses: -(2(-2V+10)V), so:

2(-2V+10)V

We multiply parentheses

-4V^2+20V

Back to the equation:

-(-4V^2+20V)


We get rid of parentheses

4V^2-20V+V=0

We add all the numbers together, and all the variables

4V^2-19V=0

a = 4; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·4·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*4}=\frac{0}{8}
=0
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*4}=\frac{38}{8}
=4+3/4
$