3/3x=2x+1

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

3/3x=2x+1

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

3/3x-2x-1=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -6; b = -3; c = +3;
Δ = b2-4ac
Δ = -32-4·(-6)·3
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-9}{2*-6}=\frac{-6}{-12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9}{2*-6}=\frac{12}{-12}
=-1
$