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

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



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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We multiply parentheses ..

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

We add all the numbers together, and all the variables

8x^2+(+4x^2-90x-48x+1080)-138x=0

We get rid of parentheses

8x^2+4x^2-90x-48x-138x+1080=0

We add all the numbers together, and all the variables

12x^2-276x+1080=0

a = 12; b = -276; c = +1080;
Δ = b2-4ac
Δ = -2762-4·12·1080
Δ = 24336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24336}=156$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-276)-156}{2*12}=\frac{120}{24}
=5
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-276)+156}{2*12}=\frac{432}{24}
=18
$

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