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

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

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

We move all terms to the left:

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

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-8x*3x-x*3x+5*3x+4*3x+2=0

Wy multiply elements

-24x^2-3x^2+15x+12x+2=0

We add all the numbers together, and all the variables

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

a = -27; b = 27; c = +2;
Δ = b2-4ac
Δ = 272-4·(-27)·2
Δ = 945
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:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{105}}{2*-27}=\frac{-27-3\sqrt{105}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{105}}{2*-27}=\frac{-27+3\sqrt{105}}{-54}
$