3-3x=2/3x+6

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

3-3x=2/3x+6

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-9x^2-9x-2=0

a = -9; b = -9; c = -2;
Δ = b2-4ac
Δ = -92-4·(-9)·(-2)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3}{2*-9}=\frac{6}{-18}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3}{2*-9}=\frac{12}{-18}
=-2/3
$