2/3x-1=9-2x

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

2/3x-1=9-2x

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-27x-3x+2=0

We add all the numbers together, and all the variables

6x^2-30x+2=0

a = 6; b = -30; c = +2;
Δ = b2-4ac
Δ = -302-4·6·2
Δ = 852
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:

$\sqrt{\Delta}=\sqrt{852}=\sqrt{4*213}=\sqrt{4}*\sqrt{213}=2\sqrt{213}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{213}}{2*6}=\frac{30-2\sqrt{213}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{213}}{2*6}=\frac{30+2\sqrt{213}}{12}
$