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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2+3x+6x-1=0

We add all the numbers together, and all the variables

-6x^2+9x-1=0

a = -6; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·(-6)·(-1)
Δ = 57
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{-(9)-\sqrt{57}}{2*-6}=\frac{-9-\sqrt{57}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{57}}{2*-6}=\frac{-9+\sqrt{57}}{-12}
$