-8/3x+4x+2/3x=7

Solution for -8/3x+4x+2/3x=7 equation:

-8/3x+4x+2/3x=7

We move all terms to the left:

-8/3x+4x+2/3x-(7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4x-8/3x+2/3x-7=0

We multiply all the terms by the denominator


4x*3x-7*3x-8+2=0

We add all the numbers together, and all the variables

4x*3x-7*3x-6=0

Wy multiply elements

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