2x-4=1/3x-3

Solution for 2x-4=1/3x-3 equation:

2x-4=1/3x-3

We move all terms to the left:

2x-4-(1/3x-3)=0


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

x∈R


We get rid of parentheses

2x-1/3x+3-4=0

We multiply all the terms by the denominator


2x*3x+3*3x-4*3x-1=0

Wy multiply elements

6x^2+9x-12x-1=0

We add all the numbers together, and all the variables

6x^2-3x-1=0

a = 6; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·6·(-1)
Δ = 33
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{-(-3)-\sqrt{33}}{2*6}=\frac{3-\sqrt{33}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{33}}{2*6}=\frac{3+\sqrt{33}}{12}
$