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

Solution for 2(3x)-4=4/6x equation:

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

We move all terms to the left:

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


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

23x-(+4/6x)-4=0

We get rid of parentheses

23x-4/6x-4=0

We multiply all the terms by the denominator


23x*6x-4*6x-4=0

Wy multiply elements

138x^2-24x-4=0

a = 138; b = -24; c = -4;
Δ = b2-4ac
Δ = -242-4·138·(-4)
Δ = 2784
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:

$\sqrt{\Delta}=\sqrt{2784}=\sqrt{16*174}=\sqrt{16}*\sqrt{174}=4\sqrt{174}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{174}}{2*138}=\frac{24-4\sqrt{174}}{276}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{174}}{2*138}=\frac{24+4\sqrt{174}}{276}
$