V(x)=(21-2x)(29.7-2x)

Solution for V(x)=(21-2x)(29.7-2x) equation:

(V)=(21-2V)(29.7-2V)

We move all terms to the left:

(V)-((21-2V)(29.7-2V))=0

We add all the numbers together, and all the variables

V-((-2V+21)(-2V+29.7))=0

We multiply parentheses ..

-((+4V^2-59.4V-42V+623.7))+V=0


We calculate terms in parentheses: -((+4V^2-59.4V-42V+623.7)), so:

(+4V^2-59.4V-42V+623.7)

We get rid of parentheses

4V^2-59.4V-42V+623.7

We add all the numbers together, and all the variables

4V^2-101.4V+623.7

Back to the equation:

-(4V^2-101.4V+623.7)


We add all the numbers together, and all the variables

V-(4V^2-101.4V+623.7)=0

We get rid of parentheses

-4V^2+V+101.4V-623.7=0

We add all the numbers together, and all the variables

-4V^2+102.4V-623.7=0

a = -4; b = 102.4; c = -623.7;
Δ = b2-4ac
Δ = 102.42-4·(-4)·(-623.7)
Δ = 506.56
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{-(102.4)-\sqrt{506.56}}{2*-4}=\frac{-102.4-\sqrt{506.56}}{-8}
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(102.4)+\sqrt{506.56}}{2*-4}=\frac{-102.4+\sqrt{506.56}}{-8}
$