A(x)=(1-x)(6x-8)+16-9x2

Solution for A(x)=(1-x)(6x-8)+16-9x2 equation:

(A)=(1-A)(6A-8)+16-9A^2

We move all terms to the left:

(A)-((1-A)(6A-8)+16-9A^2)=0

We add all the numbers together, and all the variables

-((-1A+1)(6A-8)+16-9A^2)+A=0

We multiply parentheses ..

-((-6A^2+8A+6A-8)+16-9A^2)+A=0


We calculate terms in parentheses: -((-6A^2+8A+6A-8)+16-9A^2), so:

(-6A^2+8A+6A-8)+16-9A^2

determiningTheFunctionDomain
(-6A^2+8A+6A-8)-9A^2+16

We add all the numbers together, and all the variables

-9A^2+(-6A^2+8A+6A-8)+16

We get rid of parentheses

-9A^2-6A^2+8A+6A-8+16

We add all the numbers together, and all the variables

-15A^2+14A+8

Back to the equation:

-(-15A^2+14A+8)


We get rid of parentheses

15A^2-14A+A-8=0

We add all the numbers together, and all the variables

15A^2-13A-8=0

a = 15; b = -13; c = -8;
Δ = b2-4ac
Δ = -132-4·15·(-8)
Δ = 649
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{-(-13)-\sqrt{649}}{2*15}=\frac{13-\sqrt{649}}{30}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{649}}{2*15}=\frac{13+\sqrt{649}}{30}
$