(20-2x)*(30-2x)=184

Solution for (20-2x)*(30-2x)=184 equation:

(20-2x)(30-2x)=184

We move all terms to the left:

(20-2x)(30-2x)-(184)=0

We add all the numbers together, and all the variables

(-2x+20)(-2x+30)-184=0

We multiply parentheses ..

(+4x^2-60x-40x+600)-184=0

We get rid of parentheses

4x^2-60x-40x+600-184=0

We add all the numbers together, and all the variables

4x^2-100x+416=0

a = 4; b = -100; c = +416;
Δ = b2-4ac
Δ = -1002-4·4·416
Δ = 3344
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:

$\sqrt{\Delta}=\sqrt{3344}=\sqrt{16*209}=\sqrt{16}*\sqrt{209}=4\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{209}}{2*4}=\frac{100-4\sqrt{209}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{209}}{2*4}=\frac{100+4\sqrt{209}}{8}
$