3x-2=-1/3x+6

Solution for 3x-2=-1/3x+6 equation:

3x-2=-1/3x+6

We move all terms to the left:

3x-2-(-1/3x+6)=0


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

x∈R


We get rid of parentheses

3x+1/3x-6-2=0

We multiply all the terms by the denominator


3x*3x-6*3x-2*3x+1=0

Wy multiply elements

9x^2-18x-6x+1=0

We add all the numbers together, and all the variables

9x^2-24x+1=0

a = 9; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·9·1
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{15}}{2*9}=\frac{24-6\sqrt{15}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{15}}{2*9}=\frac{24+6\sqrt{15}}{18}
$