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

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

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

We move all terms to the left:

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


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

2x^2-1x-(+1/6)=0

We get rid of parentheses

2x^2-1x-1/6=0

We multiply all the terms by the denominator


2x^2*6-1x*6-1=0

Wy multiply elements

12x^2-6x-1=0

a = 12; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·12·(-1)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{21}}{2*12}=\frac{6-2\sqrt{21}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{21}}{2*12}=\frac{6+2\sqrt{21}}{24}
$