A(x)=(11-22x)(8.5-2x)

Solution for A(x)=(11-22x)(8.5-2x) equation:

(A)=(11-22A)(8.5-2A)

We move all terms to the left:

(A)-((11-22A)(8.5-2A))=0

We add all the numbers together, and all the variables

A-((-22A+11)(-2A+8.5))=0

We multiply parentheses ..

-((+44A^2-187A-22A+93.5))+A=0


We calculate terms in parentheses: -((+44A^2-187A-22A+93.5)), so:

(+44A^2-187A-22A+93.5)

We get rid of parentheses

44A^2-187A-22A+93.5

We add all the numbers together, and all the variables

44A^2-209A+93.5

Back to the equation:

-(44A^2-209A+93.5)


We add all the numbers together, and all the variables

A-(44A^2-209A+93.5)=0

We get rid of parentheses

-44A^2+A+209A-93.5=0

We add all the numbers together, and all the variables

-44A^2+210A-93.5=0

a = -44; b = 210; c = -93.5;
Δ = b2-4ac
Δ = 2102-4·(-44)·(-93.5)
Δ = 27644
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{27644}=\sqrt{4*6911}=\sqrt{4}*\sqrt{6911}=2\sqrt{6911}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(210)-2\sqrt{6911}}{2*-44}=\frac{-210-2\sqrt{6911}}{-88}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(210)+2\sqrt{6911}}{2*-44}=\frac{-210+2\sqrt{6911}}{-88}
$