(18+2x)(24+2x)=832

Solution for (18+2x)(24+2x)=832 equation:

(18+2x)(24+2x)=832

We move all terms to the left:

(18+2x)(24+2x)-(832)=0

We add all the numbers together, and all the variables

(2x+18)(2x+24)-832=0

We multiply parentheses ..

(+4x^2+48x+36x+432)-832=0

We get rid of parentheses

4x^2+48x+36x+432-832=0

We add all the numbers together, and all the variables

4x^2+84x-400=0

a = 4; b = 84; c = -400;
Δ = b2-4ac
Δ = 842-4·4·(-400)
Δ = 13456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13456}=116$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-116}{2*4}=\frac{-200}{8}
=-25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+116}{2*4}=\frac{32}{8}
=4
$