V=(15-2x)(8-2x)

Solution for V=(15-2x)(8-2x) equation:

=(15-2V)(8-2V)

We move all terms to the left:

-((15-2V)(8-2V))=0

We add all the numbers together, and all the variables

-((-2V+15)(-2V+8))=0

We multiply parentheses ..

-((+4V^2-16V-30V+120))=0


We calculate terms in parentheses: -((+4V^2-16V-30V+120)), so:

(+4V^2-16V-30V+120)

We get rid of parentheses

4V^2-16V-30V+120

We add all the numbers together, and all the variables

4V^2-46V+120

Back to the equation:

-(4V^2-46V+120)


We get rid of parentheses

-4V^2+46V-120=0

a = -4; b = 46; c = -120;
Δ = b2-4ac
Δ = 462-4·(-4)·(-120)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-14}{2*-4}=\frac{-60}{-8}
=7+1/2
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+14}{2*-4}=\frac{-32}{-8}
=+4
$