2/3x-3=8-3x

Solution for 2/3x-3=8-3x equation:

2/3x-3=8-3x

We move all terms to the left:

2/3x-3-(8-3x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(-3x+8)-3=0

We get rid of parentheses

2/3x+3x-8-3=0

We multiply all the terms by the denominator


3x*3x-8*3x-3*3x+2=0

Wy multiply elements

9x^2-24x-9x+2=0

We add all the numbers together, and all the variables

9x^2-33x+2=0

a = 9; b = -33; c = +2;
Δ = b2-4ac
Δ = -332-4·9·2
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3\sqrt{113}}{2*9}=\frac{33-3\sqrt{113}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3\sqrt{113}}{2*9}=\frac{33+3\sqrt{113}}{18}
$