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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


2x/54x^2+27x/54x^2+4x/54x^2+1=0

We multiply all the terms by the denominator


2x+27x+4x+1*54x^2=0

We add all the numbers together, and all the variables

33x+1*54x^2=0

Wy multiply elements

54x^2+33x=0

a = 54; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·54·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*54}=\frac{-66}{108}
=-11/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*54}=\frac{0}{108}
=0
$