4/6x-2=x-2

Solution for 4/6x-2=x-2 equation:

4/6x-2=x-2

We move all terms to the left:

4/6x-2-(x-2)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

4/6x-x+2-2=0

We multiply all the terms by the denominator


-x*6x+2*6x-2*6x+4=0

Wy multiply elements

-6x^2+12x-12x+4=0

We add all the numbers together, and all the variables

-6x^2+4=0

a = -6; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-6)·4
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*-6}=\frac{0-4\sqrt{6}}{-12}
=-\frac{4\sqrt{6}}{-12}
=-\frac{\sqrt{6}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*-6}=\frac{0+4\sqrt{6}}{-12}
=\frac{4\sqrt{6}}{-12}
=\frac{\sqrt{6}}{-3}
$