(2x+8)(24+x)=96

Solution for (2x+8)(24+x)=96 equation:

(2x+8)(24+x)=96

We move all terms to the left:

(2x+8)(24+x)-(96)=0

We add all the numbers together, and all the variables

(2x+8)(x+24)-96=0

We multiply parentheses ..

(+2x^2+48x+8x+192)-96=0

We get rid of parentheses

2x^2+48x+8x+192-96=0

We add all the numbers together, and all the variables

2x^2+56x+96=0

a = 2; b = 56; c = +96;
Δ = b2-4ac
Δ = 562-4·2·96
Δ = 2368
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2368}=\sqrt{64*37}=\sqrt{64}*\sqrt{37}=8\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-8\sqrt{37}}{2*2}=\frac{-56-8\sqrt{37}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+8\sqrt{37}}{2*2}=\frac{-56+8\sqrt{37}}{4}
$