x=1/3x-6

Solution for x=1/3x-6 equation:

x=1/3x-6

We move all terms to the left:

x-(1/3x-6)=0


Domain of the equation: 3x-6)!=0

x∈R


We get rid of parentheses

x-1/3x+6=0

We multiply all the terms by the denominator


x*3x+6*3x-1=0

Wy multiply elements

3x^2+18x-1=0

a = 3; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·3·(-1)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4\sqrt{21}}{2*3}=\frac{-18-4\sqrt{21}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4\sqrt{21}}{2*3}=\frac{-18+4\sqrt{21}}{6}
$