(3x-3)/(x(2)-3x)=3

Solution for (3x-3)/(x(2)-3x)=3 equation:

(3x-3)/(x(2)-3x)=3

We move all terms to the left:

(3x-3)/(x(2)-3x)-(3)=0


Domain of the equation: (x2-3x)!=0

x∈R


We add all the numbers together, and all the variables

(3x-3)/(+x^2-3x)-3=0

We multiply all the terms by the denominator


-3*(+x^2-3x)+(3x-3)=0

We multiply parentheses

-3x^2+9x+(3x-3)=0

We get rid of parentheses

-3x^2+9x+3x-3=0

We add all the numbers together, and all the variables

-3x^2+12x-3=0

a = -3; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·(-3)·(-3)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{3}}{2*-3}=\frac{-12-6\sqrt{3}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{3}}{2*-3}=\frac{-12+6\sqrt{3}}{-6}
$