x=1/3x+12

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

x=1/3x+12

We move all terms to the left:

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


Domain of the equation: 3x+12)!=0

x∈R


We get rid of parentheses

x-1/3x-12=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2-36x-1=0

a = 3; b = -36; c = -1;
Δ = b2-4ac
Δ = -362-4·3·(-1)
Δ = 1308
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:

$\sqrt{\Delta}=\sqrt{1308}=\sqrt{4*327}=\sqrt{4}*\sqrt{327}=2\sqrt{327}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{327}}{2*3}=\frac{36-2\sqrt{327}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{327}}{2*3}=\frac{36+2\sqrt{327}}{6}
$