V(x)=(8-2x)(5-2x)

Solution for V(x)=(8-2x)(5-2x) equation:

(V)=(8-2V)(5-2V)

We move all terms to the left:

(V)-((8-2V)(5-2V))=0

We add all the numbers together, and all the variables

V-((-2V+8)(-2V+5))=0

We multiply parentheses ..

-((+4V^2-10V-16V+40))+V=0


We calculate terms in parentheses: -((+4V^2-10V-16V+40)), so:

(+4V^2-10V-16V+40)

We get rid of parentheses

4V^2-10V-16V+40

We add all the numbers together, and all the variables

4V^2-26V+40

Back to the equation:

-(4V^2-26V+40)


We add all the numbers together, and all the variables

V-(4V^2-26V+40)=0

We get rid of parentheses

-4V^2+V+26V-40=0

We add all the numbers together, and all the variables

-4V^2+27V-40=0

a = -4; b = 27; c = -40;
Δ = b2-4ac
Δ = 272-4·(-4)·(-40)
Δ = 89
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{-(27)-\sqrt{89}}{2*-4}=\frac{-27-\sqrt{89}}{-8}
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{89}}{2*-4}=\frac{-27+\sqrt{89}}{-8}
$