V(x)=(10-2x)(8-2x)

Solution for V(x)=(10-2x)(8-2x) equation:

(V)=(10-2V)(8-2V)

We move all terms to the left:

(V)-((10-2V)(8-2V))=0

We add all the numbers together, and all the variables

V-((-2V+10)(-2V+8))=0

We multiply parentheses ..

-((+4V^2-16V-20V+80))+V=0


We calculate terms in parentheses: -((+4V^2-16V-20V+80)), so:

(+4V^2-16V-20V+80)

We get rid of parentheses

4V^2-16V-20V+80

We add all the numbers together, and all the variables

4V^2-36V+80

Back to the equation:

-(4V^2-36V+80)


We add all the numbers together, and all the variables

V-(4V^2-36V+80)=0

We get rid of parentheses

-4V^2+V+36V-80=0

We add all the numbers together, and all the variables

-4V^2+37V-80=0

a = -4; b = 37; c = -80;
Δ = b2-4ac
Δ = 372-4·(-4)·(-80)
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{-(37)-\sqrt{89}}{2*-4}=\frac{-37-\sqrt{89}}{-8}
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{89}}{2*-4}=\frac{-37+\sqrt{89}}{-8}
$