V(x)=(21-2x)*(30-2x)

Solution for V(x)=(21-2x)*(30-2x) equation:

(V)=(21-2V)(30-2V)

We move all terms to the left:

(V)-((21-2V)(30-2V))=0

We add all the numbers together, and all the variables

V-((-2V+21)(-2V+30))=0

We multiply parentheses ..

-((+4V^2-60V-42V+630))+V=0


We calculate terms in parentheses: -((+4V^2-60V-42V+630)), so:

(+4V^2-60V-42V+630)

We get rid of parentheses

4V^2-60V-42V+630

We add all the numbers together, and all the variables

4V^2-102V+630

Back to the equation:

-(4V^2-102V+630)


We add all the numbers together, and all the variables

V-(4V^2-102V+630)=0

We get rid of parentheses

-4V^2+V+102V-630=0

We add all the numbers together, and all the variables

-4V^2+103V-630=0

a = -4; b = 103; c = -630;
Δ = b2-4ac
Δ = 1032-4·(-4)·(-630)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(103)-23}{2*-4}=\frac{-126}{-8}
=15+3/4
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(103)+23}{2*-4}=\frac{-80}{-8}
=+10
$