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

Solution for 4/3x-2(x+4)=x equation:

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+4/3x-2(x+4)=0

We multiply parentheses

-1x+4/3x-2x-8=0

We multiply all the terms by the denominator


-1x*3x-2x*3x-8*3x+4=0

Wy multiply elements

-3x^2-6x^2-24x+4=0

We add all the numbers together, and all the variables

-9x^2-24x+4=0

a = -9; b = -24; c = +4;
Δ = b2-4ac
Δ = -242-4·(-9)·4
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{5}}{2*-9}=\frac{24-12\sqrt{5}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{5}}{2*-9}=\frac{24+12\sqrt{5}}{-18}
$