2-3x=9-2(-1/3x+3)

Solution for 2-3x=9-2(-1/3x+3) equation:

2-3x=9-2(-1/3x+3)

We move all terms to the left:

2-3x-(9-2(-1/3x+3))=0


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

x∈R


We multiply all the terms by the denominator


-3x*3x+2*3x-1+3))-(9-2(+3))=0

We add all the numbers together, and all the variables

-3x*3x+2*3x-1+3))-(9-23)=0

We add all the numbers together, and all the variables

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

Wy multiply elements

-9x^2+6x=0

a = -9; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-9)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-9}=\frac{-12}{-18}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-9}=\frac{0}{-18}
=0
$