-1/3x=-2x-1

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

-1/3x=-2x-1

We move all terms to the left:

-1/3x-(-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=0

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2+3x-1=0

a = 6; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·6·(-1)
Δ = 33
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{33}}{2*6}=\frac{-3-\sqrt{33}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{33}}{2*6}=\frac{-3+\sqrt{33}}{12}
$