(24+x)(16+x)=1140

Solution for (24+x)(16+x)=1140 equation:

(24+x)(16+x)=1140

We move all terms to the left:

(24+x)(16+x)-(1140)=0

We add all the numbers together, and all the variables

(x+24)(x+16)-1140=0

We multiply parentheses ..

(+x^2+16x+24x+384)-1140=0

We get rid of parentheses

x^2+16x+24x+384-1140=0

We add all the numbers together, and all the variables

x^2+40x-756=0

a = 1; b = 40; c = -756;
Δ = b2-4ac
Δ = 402-4·1·(-756)
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-68}{2*1}=\frac{-108}{2}
=-54
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+68}{2*1}=\frac{28}{2}
=14
$