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+2=0

a = -6; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-6)·2
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*-6}=\frac{0-4\sqrt{3}}{-12}
=-\frac{4\sqrt{3}}{-12}
=-\frac{\sqrt{3}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*-6}=\frac{0+4\sqrt{3}}{-12}
=\frac{4\sqrt{3}}{-12}
=\frac{\sqrt{3}}{-3}
$