(30-2x)(20-2x)=416x^2

Solution for (30-2x)(20-2x)=416x^2 equation:

(30-2x)(20-2x)=416x^2

We move all terms to the left:

(30-2x)(20-2x)-(416x^2)=0

determiningTheFunctionDomain
-416x^2+(30-2x)(20-2x)=0

We add all the numbers together, and all the variables

-416x^2+(-2x+30)(-2x+20)=0

We multiply parentheses ..

-416x^2+(+4x^2-40x-60x+600)=0

We get rid of parentheses

-416x^2+4x^2-40x-60x+600=0

We add all the numbers together, and all the variables

-412x^2-100x+600=0

a = -412; b = -100; c = +600;
Δ = b2-4ac
Δ = -1002-4·(-412)·600
Δ = 998800
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:

$\sqrt{\Delta}=\sqrt{998800}=\sqrt{400*2497}=\sqrt{400}*\sqrt{2497}=20\sqrt{2497}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{2497}}{2*-412}=\frac{100-20\sqrt{2497}}{-824}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{2497}}{2*-412}=\frac{100+20\sqrt{2497}}{-824}
$