1/3x+1=-6/4x-2

Solution for 1/3x+1=-6/4x-2 equation:

1/3x+1=-6/4x-2

We move all terms to the left:

1/3x+1-(-6/4x-2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x-2)!=0

x∈R


We get rid of parentheses

1/3x+6/4x+2+1=0

We calculate fractions


4x/12x^2+18x/12x^2+2+1=0

We add all the numbers together, and all the variables

4x/12x^2+18x/12x^2+3=0

We multiply all the terms by the denominator


4x+18x+3*12x^2=0

We add all the numbers together, and all the variables

22x+3*12x^2=0

Wy multiply elements

36x^2+22x=0

a = 36; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·36·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*36}=\frac{-44}{72}
=-11/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*36}=\frac{0}{72}
=0
$