(20+2x)(30+2x)=2400

Solution for (20+2x)(30+2x)=2400 equation:

(20+2x)(30+2x)=2400

We move all terms to the left:

(20+2x)(30+2x)-(2400)=0

We add all the numbers together, and all the variables

(2x+20)(2x+30)-2400=0

We multiply parentheses ..

(+4x^2+60x+40x+600)-2400=0

We get rid of parentheses

4x^2+60x+40x+600-2400=0

We add all the numbers together, and all the variables

4x^2+100x-1800=0

a = 4; b = 100; c = -1800;
Δ = b2-4ac
Δ = 1002-4·4·(-1800)
Δ = 38800
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:

$\sqrt{\Delta}=\sqrt{38800}=\sqrt{400*97}=\sqrt{400}*\sqrt{97}=20\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{97}}{2*4}=\frac{-100-20\sqrt{97}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{97}}{2*4}=\frac{-100+20\sqrt{97}}{8}
$