-8/3x+4x+9=-2/3x-1+3

Solution for -8/3x+4x+9=-2/3x-1+3 equation:

-8/3x+4x+9=-2/3x-1+3

We move all terms to the left:

-8/3x+4x+9-(-2/3x-1+3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3x-1+3)!=0

We move all terms containing x to the left, all other terms to the right

3x+3)!=1

x∈R


We add all the numbers together, and all the variables

-8/3x+4x-(-2/3x+2)+9=0

We add all the numbers together, and all the variables

4x-8/3x-(-2/3x+2)+9=0

We get rid of parentheses

4x-8/3x+2/3x-2+9=0

We multiply all the terms by the denominator


4x*3x-2*3x+9*3x-8+2=0

We add all the numbers together, and all the variables

4x*3x-2*3x+9*3x-6=0

Wy multiply elements

12x^2-6x+27x-6=0

We add all the numbers together, and all the variables

12x^2+21x-6=0

a = 12; b = 21; c = -6;
Δ = b2-4ac
Δ = 212-4·12·(-6)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-27}{2*12}=\frac{-48}{24}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+27}{2*12}=\frac{6}{24}
=1/4
$