(1-2x)+2x(1-x)+(1-x)(1-2x)(18)=2

Solution for (1-2x)+2x(1-x)+(1-x)(1-2x)(18)=2 equation:

(1-2x)+2x(1-x)+(1-x)(1-2x)(18)=2

We move all terms to the left:

(1-2x)+2x(1-x)+(1-x)(1-2x)(18)-(2)=0

We add all the numbers together, and all the variables

(-2x+1)+2x(-1x+1)+(-1x+1)(-2x+1)18-2=0

We multiply parentheses

-2x^2+(-2x+1)+2x+(-1x+1)(-2x+1)18-2=0

We get rid of parentheses

-2x^2-2x+2x+(-1x+1)(-2x+1)18+1-2=0

We multiply parentheses ..

-2x^2+(+2x^2-1x-2x+1)18-2x+2x+1-2=0

We add all the numbers together, and all the variables

-2x^2+(+2x^2-1x-2x+1)18-1=0

We multiply parentheses

-2x^2+36x^2-18x-36x+18-1=0

We add all the numbers together, and all the variables

34x^2-54x+17=0

a = 34; b = -54; c = +17;
Δ = b2-4ac
Δ = -542-4·34·17
Δ = 604
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:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{151}}{2*34}=\frac{54-2\sqrt{151}}{68}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{151}}{2*34}=\frac{54+2\sqrt{151}}{68}
$