(2x+24)(2x+16)=1584

Solution for (2x+24)(2x+16)=1584 equation:

(2x+24)(2x+16)=1584

We move all terms to the left:

(2x+24)(2x+16)-(1584)=0

We multiply parentheses ..

(+4x^2+32x+48x+384)-1584=0

We get rid of parentheses

4x^2+32x+48x+384-1584=0

We add all the numbers together, and all the variables

4x^2+80x-1200=0

a = 4; b = 80; c = -1200;
Δ = b2-4ac
Δ = 802-4·4·(-1200)
Δ = 25600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25600}=160$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-160}{2*4}=\frac{-240}{8}
=-30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+160}{2*4}=\frac{80}{8}
=10
$