A(x)=x(50-5x)

Solution for A(x)=x(50-5x) equation:

(A)=A(50-5A)

We move all terms to the left:

(A)-(A(50-5A))=0

We add all the numbers together, and all the variables

A-(A(-5A+50))=0


We calculate terms in parentheses: -(A(-5A+50)), so:

A(-5A+50)

We multiply parentheses

-5A^2+50A

Back to the equation:

-(-5A^2+50A)


We get rid of parentheses

5A^2-50A+A=0

We add all the numbers together, and all the variables

5A^2-49A=0

a = 5; b = -49; c = 0;
Δ = b2-4ac
Δ = -492-4·5·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-49}{2*5}=\frac{0}{10}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+49}{2*5}=\frac{98}{10}
=9+4/5
$