A(x)=(20+2x)(30+2x)

Solution for A(x)=(20+2x)(30+2x) equation:

(A)=(20+2A)(30+2A)

We move all terms to the left:

(A)-((20+2A)(30+2A))=0

We add all the numbers together, and all the variables

A-((2A+20)(2A+30))=0

We multiply parentheses ..

-((+4A^2+60A+40A+600))+A=0


We calculate terms in parentheses: -((+4A^2+60A+40A+600)), so:

(+4A^2+60A+40A+600)

We get rid of parentheses

4A^2+60A+40A+600

We add all the numbers together, and all the variables

4A^2+100A+600

Back to the equation:

-(4A^2+100A+600)


We add all the numbers together, and all the variables

A-(4A^2+100A+600)=0

We get rid of parentheses

-4A^2+A-100A-600=0

We add all the numbers together, and all the variables

-4A^2-99A-600=0

a = -4; b = -99; c = -600;
Δ = b2-4ac
Δ = -992-4·(-4)·(-600)
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-\sqrt{201}}{2*-4}=\frac{99-\sqrt{201}}{-8}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+\sqrt{201}}{2*-4}=\frac{99+\sqrt{201}}{-8}
$