2x-128=2/3x

Solution for 2x-128=2/3x equation:

2x-128=2/3x

We move all terms to the left:

2x-128-(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

2x-(+2/3x)-128=0

We get rid of parentheses

2x-2/3x-128=0

We multiply all the terms by the denominator


2x*3x-128*3x-2=0

Wy multiply elements

6x^2-384x-2=0

a = 6; b = -384; c = -2;
Δ = b2-4ac
Δ = -3842-4·6·(-2)
Δ = 147504
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:

$\sqrt{\Delta}=\sqrt{147504}=\sqrt{16*9219}=\sqrt{16}*\sqrt{9219}=4\sqrt{9219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-384)-4\sqrt{9219}}{2*6}=\frac{384-4\sqrt{9219}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-384)+4\sqrt{9219}}{2*6}=\frac{384+4\sqrt{9219}}{12}
$