A=x(5-x)

Solution for A=x(5-x) equation:

=A(5-A)

We move all terms to the left:

-(A(5-A))=0

We add all the numbers together, and all the variables

-(A(-1A+5))=0


We calculate terms in parentheses: -(A(-1A+5)), so:

A(-1A+5)

We multiply parentheses

-1A^2+5A

Back to the equation:

-(-1A^2+5A)


We get rid of parentheses

1A^2-5A=0

We add all the numbers together, and all the variables

A^2-5A=0

a = 1; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·1·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*1}=\frac{0}{2}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*1}=\frac{10}{2}
=5
$