A(x)=(3x-2)(x+9)

Solution for A(x)=(3x-2)(x+9) equation:

(A)=(3A-2)(A+9)

We move all terms to the left:

(A)-((3A-2)(A+9))=0

We multiply parentheses ..

-((+3A^2+27A-2A-18))+A=0


We calculate terms in parentheses: -((+3A^2+27A-2A-18)), so:

(+3A^2+27A-2A-18)

We get rid of parentheses

3A^2+27A-2A-18

We add all the numbers together, and all the variables

3A^2+25A-18

Back to the equation:

-(3A^2+25A-18)


We add all the numbers together, and all the variables

A-(3A^2+25A-18)=0

We get rid of parentheses

-3A^2+A-25A+18=0

We add all the numbers together, and all the variables

-3A^2-24A+18=0

a = -3; b = -24; c = +18;
Δ = b2-4ac
Δ = -242-4·(-3)·18
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{22}}{2*-3}=\frac{24-6\sqrt{22}}{-6}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{22}}{2*-3}=\frac{24+6\sqrt{22}}{-6}
$