X(4-x)=(1-x)(1-x)

Solution for X(4-x)=(1-x)(1-x) equation:

X(4-X)=(1-X)(1-X)

We move all terms to the left:

X(4-X)-((1-X)(1-X))=0

We add all the numbers together, and all the variables

X(-1X+4)-((-1X+1)(-1X+1))=0

We multiply parentheses

-1X^2+4X-((-1X+1)(-1X+1))=0

We multiply parentheses ..

-1X^2-((+X^2-1X-1X+1))+4X=0


We calculate terms in parentheses: -((+X^2-1X-1X+1)), so:

(+X^2-1X-1X+1)

We get rid of parentheses

X^2-1X-1X+1

We add all the numbers together, and all the variables

X^2-2X+1

Back to the equation:

-(X^2-2X+1)


We add all the numbers together, and all the variables

-1X^2+4X-(X^2-2X+1)=0

We get rid of parentheses

-1X^2-X^2+4X+2X-1=0

We add all the numbers together, and all the variables

-2X^2+6X-1=0

a = -2; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·(-2)·(-1)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{7}}{2*-2}=\frac{-6-2\sqrt{7}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{7}}{2*-2}=\frac{-6+2\sqrt{7}}{-4}
$