-8+2/3x+4=2x-5x-x

Solution for -8+2/3x+4=2x-5x-x equation:

-8+2/3x+4=2x-5x-x

We move all terms to the left:

-8+2/3x+4-(2x-5x-x)=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-(-4x)-8+4=0

We add all the numbers together, and all the variables

2/3x-(-4x)-4=0

We get rid of parentheses

2/3x+4x-4=0

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-12x+2=0

a = 12; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·12·2
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{3}}{2*12}=\frac{12-4\sqrt{3}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{3}}{2*12}=\frac{12+4\sqrt{3}}{24}
$