5/3x+2=2x+1

Solution for 5/3x+2=2x+1 equation:

5/3x+2=2x+1

We move all terms to the left:

5/3x+2-(2x+1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

5/3x-2x-1+2=0

We multiply all the terms by the denominator


-2x*3x-1*3x+2*3x+5=0

Wy multiply elements

-6x^2-3x+6x+5=0

We add all the numbers together, and all the variables

-6x^2+3x+5=0

a = -6; b = 3; c = +5;
Δ = b2-4ac
Δ = 32-4·(-6)·5
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{129}}{2*-6}=\frac{-3-\sqrt{129}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{129}}{2*-6}=\frac{-3+\sqrt{129}}{-12}
$