3x-2/3x-1=3

Solution for 3x-2/3x-1=3 equation:

3x-2/3x-1=3

We move all terms to the left:

3x-2/3x-1-(3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3x-2/3x-4=0

We multiply all the terms by the denominator


3x*3x-4*3x-2=0

Wy multiply elements

9x^2-12x-2=0

a = 9; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·9·(-2)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{6}}{2*9}=\frac{12-6\sqrt{6}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{6}}{2*9}=\frac{12+6\sqrt{6}}{18}
$