2/3x+1=2x-1

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

2/3x+1=2x-1

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2+3x+3x+2=0

We add all the numbers together, and all the variables

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

a = -6; b = 6; c = +2;
Δ = b2-4ac
Δ = 62-4·(-6)·2
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*-6}=\frac{-6-2\sqrt{21}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{21}}{2*-6}=\frac{-6+2\sqrt{21}}{-12}
$