2/3x=2x-128

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

2/3x=2x-128

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-2x+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}
$