A=4x-(x+2)(x-3)

Solution for A=4x-(x+2)(x-3) equation:

=4A-(A+2)(A-3)

We move all terms to the left:

-(4A-(A+2)(A-3))=0

We multiply parentheses ..

-(4A-(+A^2-3A+2A-6))=0


We calculate terms in parentheses: -(4A-(+A^2-3A+2A-6)), so:

4A-(+A^2-3A+2A-6)

determiningTheFunctionDomain
-(+A^2-3A+2A-6)+4A

We get rid of parentheses

-A^2+3A-2A+4A+6

We add all the numbers together, and all the variables

-1A^2+5A+6

Back to the equation:

-(-1A^2+5A+6)


We get rid of parentheses

1A^2-5A-6=0

We add all the numbers together, and all the variables

A^2-5A-6=0

a = 1; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·1·(-6)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*1}=\frac{-2}{2}
=-1
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*1}=\frac{12}{2}
=6
$