-2(45-2x)x-2(24-2x)+(24-2x)(45-2x)=0

Solution for -2(45-2x)x-2(24-2x)+(24-2x)(45-2x)=0 equation:

-2(45-2x)x-2(24-2x)+(24-2x)(45-2x)=0

We add all the numbers together, and all the variables

-2(-2x+45)x-2(-2x+24)+(-2x+24)(-2x+45)=0

We multiply parentheses

4x^2-90x+4x+(-2x+24)(-2x+45)-48=0

We multiply parentheses ..

4x^2+(+4x^2-90x-48x+1080)-90x+4x-48=0

We add all the numbers together, and all the variables

4x^2+(+4x^2-90x-48x+1080)-86x-48=0

We get rid of parentheses

4x^2+4x^2-90x-48x-86x+1080-48=0

We add all the numbers together, and all the variables

8x^2-224x+1032=0

a = 8; b = -224; c = +1032;
Δ = b2-4ac
Δ = -2242-4·8·1032
Δ = 17152
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:

$\sqrt{\Delta}=\sqrt{17152}=\sqrt{256*67}=\sqrt{256}*\sqrt{67}=16\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-224)-16\sqrt{67}}{2*8}=\frac{224-16\sqrt{67}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-224)+16\sqrt{67}}{2*8}=\frac{224+16\sqrt{67}}{16}
$