24(18+x)-24(18-x)=(18-x)(18+x)

Solution for 24(18+x)-24(18-x)=(18-x)(18+x) equation:

24(18+x)-24(18-x)=(18-x)(18+x)

We move all terms to the left:

24(18+x)-24(18-x)-((18-x)(18+x))=0

We add all the numbers together, and all the variables

24(x+18)-24(-1x+18)-((-1x+18)(x+18))=0

We multiply parentheses

24x+24x-((-1x+18)(x+18))+432-432=0

We multiply parentheses ..

-((-1x^2-18x+18x+324))+24x+24x+432-432=0


We calculate terms in parentheses: -((-1x^2-18x+18x+324)), so:

(-1x^2-18x+18x+324)

We get rid of parentheses

-1x^2-18x+18x+324

We add all the numbers together, and all the variables

-1x^2+324

Back to the equation:

-(-1x^2+324)


We add all the numbers together, and all the variables

-(-1x^2+324)+48x=0

We get rid of parentheses

1x^2+48x-324=0

We add all the numbers together, and all the variables

x^2+48x-324=0

a = 1; b = 48; c = -324;
Δ = b2-4ac
Δ = 482-4·1·(-324)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-60}{2*1}=\frac{-108}{2}
=-54
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+60}{2*1}=\frac{12}{2}
=6
$