12-(1/3)x=4+x

Solution for 12-(1/3)x=4+x equation:

12-(1/3)x=4+x

We move all terms to the left:

12-(1/3)x-(4+x)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+1/3)x-(x+4)+12=0

We multiply parentheses

-x^2-(x+4)+12=0

We get rid of parentheses

-x^2-x-4+12=0

We add all the numbers together, and all the variables

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

a = -1; b = -1; c = +8;
Δ = b2-4ac
Δ = -12-4·(-1)·8
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{33}}{2*-1}=\frac{1-\sqrt{33}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{33}}{2*-1}=\frac{1+\sqrt{33}}{-2}
$