V(x)=(11-2x)(17-2x)

Solution for V(x)=(11-2x)(17-2x) equation:

(V)=(11-2V)(17-2V)

We move all terms to the left:

(V)-((11-2V)(17-2V))=0

We add all the numbers together, and all the variables

V-((-2V+11)(-2V+17))=0

We multiply parentheses ..

-((+4V^2-34V-22V+187))+V=0


We calculate terms in parentheses: -((+4V^2-34V-22V+187)), so:

(+4V^2-34V-22V+187)

We get rid of parentheses

4V^2-34V-22V+187

We add all the numbers together, and all the variables

4V^2-56V+187

Back to the equation:

-(4V^2-56V+187)


We add all the numbers together, and all the variables

V-(4V^2-56V+187)=0

We get rid of parentheses

-4V^2+V+56V-187=0

We add all the numbers together, and all the variables

-4V^2+57V-187=0

a = -4; b = 57; c = -187;
Δ = b2-4ac
Δ = 572-4·(-4)·(-187)
Δ = 257
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{-(57)-\sqrt{257}}{2*-4}=\frac{-57-\sqrt{257}}{-8}
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+\sqrt{257}}{2*-4}=\frac{-57+\sqrt{257}}{-8}
$