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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

(-2x+30)(-2x+20)-33856=0

We multiply parentheses ..

(+4x^2-40x-60x+600)-33856=0

We get rid of parentheses

4x^2-40x-60x+600-33856=0

We add all the numbers together, and all the variables

4x^2-100x-33256=0

a = 4; b = -100; c = -33256;
Δ = b2-4ac
Δ = -1002-4·4·(-33256)
Δ = 542096
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:

$\sqrt{\Delta}=\sqrt{542096}=\sqrt{16*33881}=\sqrt{16}*\sqrt{33881}=4\sqrt{33881}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{33881}}{2*4}=\frac{100-4\sqrt{33881}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{33881}}{2*4}=\frac{100+4\sqrt{33881}}{8}
$