x-3/3x-1=1

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

x-3/3x-1=1

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x-3/3x-2=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2-6x-3=0

a = 3; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·3·(-3)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{2}}{2*3}=\frac{6-6\sqrt{2}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{2}}{2*3}=\frac{6+6\sqrt{2}}{6}
$