(X-1)(3x-3)=x

Solution for (X-1)(3x-3)=x equation:

(X-1)(3X-3)=X

We move all terms to the left:

(X-1)(3X-3)-(X)=0

We add all the numbers together, and all the variables

-1X+(X-1)(3X-3)=0

We multiply parentheses ..

(+3X^2-3X-3X+3)-1X=0

We get rid of parentheses

3X^2-3X-3X-1X+3=0

We add all the numbers together, and all the variables

3X^2-7X+3=0

a = 3; b = -7; c = +3;
Δ = b2-4ac
Δ = -72-4·3·3
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{13}}{2*3}=\frac{7-\sqrt{13}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{13}}{2*3}=\frac{7+\sqrt{13}}{6}
$