0.3333333x-x=12-8/3x

Solution for 0.3333333x-x=12-8/3x equation:

0.3333333x-x=12-8/3x

We move all terms to the left:

0.3333333x-x-(12-8/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

0.3333333x-x-(-8/3x+12)=0

We add all the numbers together, and all the variables

-0.6666667x-(-8/3x+12)=0

We get rid of parentheses

-0.6666667x+8/3x-12=0

We multiply all the terms by the denominator


-(0.6666667x)*3x-12*3x+8=0

We add all the numbers together, and all the variables

-(+0.6666667x)*3x-12*3x+8=0

We multiply parentheses

-0x^2-12*3x+8=0

Wy multiply elements

-0x^2-36x+8=0

We add all the numbers together, and all the variables

-1x^2-36x+8=0

a = -1; b = -36; c = +8;
Δ = b2-4ac
Δ = -362-4·(-1)·8
Δ = 1328
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:

$\sqrt{\Delta}=\sqrt{1328}=\sqrt{16*83}=\sqrt{16}*\sqrt{83}=4\sqrt{83}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{83}}{2*-1}=\frac{36-4\sqrt{83}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{83}}{2*-1}=\frac{36+4\sqrt{83}}{-2}
$