(40+x)(20+x)=1600

Solution for (40+x)(20+x)=1600 equation:

(40+x)(20+x)=1600

We move all terms to the left:

(40+x)(20+x)-(1600)=0

We add all the numbers together, and all the variables

(x+40)(x+20)-1600=0

We multiply parentheses ..

(+x^2+20x+40x+800)-1600=0

We get rid of parentheses

x^2+20x+40x+800-1600=0

We add all the numbers together, and all the variables

x^2+60x-800=0

a = 1; b = 60; c = -800;
Δ = b2-4ac
Δ = 602-4·1·(-800)
Δ = 6800
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:

$\sqrt{\Delta}=\sqrt{6800}=\sqrt{400*17}=\sqrt{400}*\sqrt{17}=20\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-20\sqrt{17}}{2*1}=\frac{-60-20\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+20\sqrt{17}}{2*1}=\frac{-60+20\sqrt{17}}{2}
$