(16+x)(24+x)=560

Solution for (16+x)(24+x)=560 equation:

(16+x)(24+x)=560

We move all terms to the left:

(16+x)(24+x)-(560)=0

We add all the numbers together, and all the variables

(x+16)(x+24)-560=0

We multiply parentheses ..

(+x^2+24x+16x+384)-560=0

We get rid of parentheses

x^2+24x+16x+384-560=0

We add all the numbers together, and all the variables

x^2+40x-176=0

a = 1; b = 40; c = -176;
Δ = b2-4ac
Δ = 402-4·1·(-176)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-48}{2*1}=\frac{-88}{2}
=-44
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+48}{2*1}=\frac{8}{2}
=4
$