4x=2/3x=

Solution for 4x=2/3x= equation:

4x=2/3x=

We move all terms to the left:

4x-(2/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4x-2/3x=0

We multiply all the terms by the denominator


4x*3x-2=0

Wy multiply elements

12x^2-2=0

a = 12; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·12·(-2)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*12}=\frac{0-4\sqrt{6}}{24}
=-\frac{4\sqrt{6}}{24}
=-\frac{\sqrt{6}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*12}=\frac{0+4\sqrt{6}}{24}
=\frac{4\sqrt{6}}{24}
=\frac{\sqrt{6}}{6}
$