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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((+4V^2-60V-60V+900))+V=0


We calculate terms in parentheses: -((+4V^2-60V-60V+900)), so:

(+4V^2-60V-60V+900)

We get rid of parentheses

4V^2-60V-60V+900

We add all the numbers together, and all the variables

4V^2-120V+900

Back to the equation:

-(4V^2-120V+900)


We add all the numbers together, and all the variables

V-(4V^2-120V+900)=0

We get rid of parentheses

-4V^2+V+120V-900=0

We add all the numbers together, and all the variables

-4V^2+121V-900=0

a = -4; b = 121; c = -900;
Δ = b2-4ac
Δ = 1212-4·(-4)·(-900)
Δ = 241
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{-(121)-\sqrt{241}}{2*-4}=\frac{-121-\sqrt{241}}{-8}
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(121)+\sqrt{241}}{2*-4}=\frac{-121+\sqrt{241}}{-8}
$