8/3x=2x+4

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

8/3x=2x+4

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

8/3x-2x-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}
$