3x-1=8-2/3x

Solution for 3x-1=8-2/3x equation:

3x-1=8-2/3x

We move all terms to the left:

3x-1-(8-2/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(-2/3x+8)-1=0

We get rid of parentheses

3x+2/3x-8-1=0

We multiply all the terms by the denominator


3x*3x-8*3x-1*3x+2=0

Wy multiply elements

9x^2-24x-3x+2=0

We add all the numbers together, and all the variables

9x^2-27x+2=0

a = 9; b = -27; c = +2;
Δ = b2-4ac
Δ = -272-4·9·2
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{73}}{2*9}=\frac{27-3\sqrt{73}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{73}}{2*9}=\frac{27+3\sqrt{73}}{18}
$