2x=4+8/3x

Solution for 2x=4+8/3x equation:

2x=4+8/3x

We move all terms to the left:

2x-(4+8/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(8/3x+4)=0

We get rid of parentheses

2x-8/3x-4=0

We multiply all the terms by the denominator


2x*3x-4*3x-8=0

Wy multiply elements

6x^2-12x-8=0

a = 6; b = -12; c = -8;
Δ = b2-4ac
Δ = -122-4·6·(-8)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{21}}{2*6}=\frac{12-4\sqrt{21}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{21}}{2*6}=\frac{12+4\sqrt{21}}{12}
$