3x-6/2x-1=2

Solution for 3x-6/2x-1=2 equation:

3x-6/2x-1=2

We move all terms to the left:

3x-6/2x-1-(2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x-6/2x-3=0

We multiply all the terms by the denominator


3x*2x-3*2x-6=0

Wy multiply elements

6x^2-6x-6=0

a = 6; b = -6; c = -6;
Δ = b2-4ac
Δ = -62-4·6·(-6)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{5}}{2*6}=\frac{6-6\sqrt{5}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{5}}{2*6}=\frac{6+6\sqrt{5}}{12}
$