(30-2x)*(20-2x)=x

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

-1x+(-2x+30)(-2x+20)=0

We multiply parentheses ..

(+4x^2-40x-60x+600)-1x=0

We get rid of parentheses

4x^2-40x-60x-1x+600=0

We add all the numbers together, and all the variables

4x^2-101x+600=0

a = 4; b = -101; c = +600;
Δ = b2-4ac
Δ = -1012-4·4·600
Δ = 601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-101)-\sqrt{601}}{2*4}=\frac{101-\sqrt{601}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-101)+\sqrt{601}}{2*4}=\frac{101+\sqrt{601}}{8}
$