A(x)=x(60-2x)

Solution for A(x)=x(60-2x) equation:

(A)=A(60-2A)

We move all terms to the left:

(A)-(A(60-2A))=0

We add all the numbers together, and all the variables

A-(A(-2A+60))=0


We calculate terms in parentheses: -(A(-2A+60)), so:

A(-2A+60)

We multiply parentheses

-2A^2+60A

Back to the equation:

-(-2A^2+60A)


We get rid of parentheses

2A^2-60A+A=0

We add all the numbers together, and all the variables

2A^2-59A=0

a = 2; b = -59; c = 0;
Δ = b2-4ac
Δ = -592-4·2·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-59}{2*2}=\frac{0}{4}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+59}{2*2}=\frac{118}{4}
=29+1/2
$