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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 1+3x)!=0

We move all terms containing x to the left, all other terms to the right

3x)!=-1

x!=-1/1

x!=-1

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-3x*6x+2*6x-2*6x+4=0

Wy multiply elements

-18x^2+12x-12x+4=0

We add all the numbers together, and all the variables

-18x^2+4=0

a = -18; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-18)·4
Δ = 288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*-18}=\frac{0-12\sqrt{2}}{-36}
=-\frac{12\sqrt{2}}{-36}
=-\frac{\sqrt{2}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*-18}=\frac{0+12\sqrt{2}}{-36}
=\frac{12\sqrt{2}}{-36}
=\frac{\sqrt{2}}{-3}
$