A=(15+x)(24+x)

Solution for A=(15+x)(24+x) equation:

=(15+A)(24+A)

We move all terms to the left:

-((15+A)(24+A))=0

We add all the numbers together, and all the variables

-((A+15)(A+24))=0

We multiply parentheses ..

-((+A^2+24A+15A+360))=0


We calculate terms in parentheses: -((+A^2+24A+15A+360)), so:

(+A^2+24A+15A+360)

We get rid of parentheses

A^2+24A+15A+360

We add all the numbers together, and all the variables

A^2+39A+360

Back to the equation:

-(A^2+39A+360)


We get rid of parentheses

-A^2-39A-360=0

We add all the numbers together, and all the variables

-1A^2-39A-360=0

a = -1; b = -39; c = -360;
Δ = b2-4ac
Δ = -392-4·(-1)·(-360)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-9}{2*-1}=\frac{30}{-2}
=-15
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+9}{2*-1}=\frac{48}{-2}
=-24
$