A(x)=5.5*x-x*x

Solution for A(x)=5.5*x-x*x equation:

(A)=5.5A-A*A

We move all terms to the left:

(A)-(5.5A-A*A)=0

We add all the numbers together, and all the variables

A-(+5.5A-A*A)=0

We get rid of parentheses

A-5.5A+A*A=0

We add all the numbers together, and all the variables

-4.5A+A*A=0

Wy multiply elements

A^2-4.5A=0

a = 1; b = -4.5; c = 0;
Δ = b2-4ac
Δ = -4.52-4·1·0
Δ = 20.25
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{-(-4.5)-\sqrt{20.25}}{2*1}=\frac{4.5-\sqrt{20.25}}{2}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.5)+\sqrt{20.25}}{2*1}=\frac{4.5+\sqrt{20.25}}{2}
$