A(12)=x(24-x)

Solution for A(12)=x(24-x) equation:

(12)=A(24-A)

We move all terms to the left:

(12)-(A(24-A))=0

We add all the numbers together, and all the variables

-(A(-1A+24))+12=0


We calculate terms in parentheses: -(A(-1A+24)), so:

A(-1A+24)

We multiply parentheses

-1A^2+24A

Back to the equation:

-(-1A^2+24A)


We get rid of parentheses

1A^2-24A+12=0

We add all the numbers together, and all the variables

A^2-24A+12=0

a = 1; b = -24; c = +12;
Δ = b2-4ac
Δ = -242-4·1·12
Δ = 528
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{33}}{2*1}=\frac{24-4\sqrt{33}}{2}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{33}}{2*1}=\frac{24+4\sqrt{33}}{2}
$