2/3x-4=x+8

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

2/3x-4=x+8

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-3x^2-36x+2=0

a = -3; b = -36; c = +2;
Δ = b2-4ac
Δ = -362-4·(-3)·2
Δ = 1320
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:

$\sqrt{\Delta}=\sqrt{1320}=\sqrt{4*330}=\sqrt{4}*\sqrt{330}=2\sqrt{330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{330}}{2*-3}=\frac{36-2\sqrt{330}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{330}}{2*-3}=\frac{36+2\sqrt{330}}{-6}
$