V(x)=(11-2x)(8.5-2x)

Solution for V(x)=(11-2x)(8.5-2x) equation:

(V)=(11-2V)(8.5-2V)

We move all terms to the left:

(V)-((11-2V)(8.5-2V))=0

We add all the numbers together, and all the variables

V-((-2V+11)(-2V+8.5))=0

We multiply parentheses ..

-((+4V^2-17V-22V+93.5))+V=0


We calculate terms in parentheses: -((+4V^2-17V-22V+93.5)), so:

(+4V^2-17V-22V+93.5)

We get rid of parentheses

4V^2-17V-22V+93.5

We add all the numbers together, and all the variables

4V^2-39V+93.5

Back to the equation:

-(4V^2-39V+93.5)


We add all the numbers together, and all the variables

V-(4V^2-39V+93.5)=0

We get rid of parentheses

-4V^2+V+39V-93.5=0

We add all the numbers together, and all the variables

-4V^2+40V-93.5=0

a = -4; b = 40; c = -93.5;
Δ = b2-4ac
Δ = 402-4·(-4)·(-93.5)
Δ = 104
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{26}}{2*-4}=\frac{-40-2\sqrt{26}}{-8}
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{26}}{2*-4}=\frac{-40+2\sqrt{26}}{-8}
$