12/3*x=32-x

Solution for 12/3*x=32-x equation:

12/3x=32-x

We move all terms to the left:

12/3x-(32-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

12/3x-(-1x+32)=0

We get rid of parentheses

12/3x+1x-32=0

We multiply all the terms by the denominator


1x*3x-32*3x+12=0

Wy multiply elements

3x^2-96x+12=0

a = 3; b = -96; c = +12;
Δ = b2-4ac
Δ = -962-4·3·12
Δ = 9072
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:

$\sqrt{\Delta}=\sqrt{9072}=\sqrt{1296*7}=\sqrt{1296}*\sqrt{7}=36\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-36\sqrt{7}}{2*3}=\frac{96-36\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+36\sqrt{7}}{2*3}=\frac{96+36\sqrt{7}}{6}
$