12+1/3x+2/3x=x

Solution for 12+1/3x+2/3x=x equation:

12+1/3x+2/3x=x

We move all terms to the left:

12+1/3x+2/3x-(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+1/3x+2/3x+12=0

We multiply all the terms by the denominator


-1x*3x+12*3x+1+2=0

We add all the numbers together, and all the variables

-1x*3x+12*3x+3=0

Wy multiply elements

-3x^2+36x+3=0

a = -3; b = 36; c = +3;
Δ = b2-4ac
Δ = 362-4·(-3)·3
Δ = 1332
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:

$\sqrt{\Delta}=\sqrt{1332}=\sqrt{36*37}=\sqrt{36}*\sqrt{37}=6\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-6\sqrt{37}}{2*-3}=\frac{-36-6\sqrt{37}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+6\sqrt{37}}{2*-3}=\frac{-36+6\sqrt{37}}{-6}
$