x/3x-2=4x+8

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

x/3x-2=4x+8

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-12x^2+x-24x-6x=0

We add all the numbers together, and all the variables

-12x^2-29x=0

a = -12; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·(-12)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*-12}=\frac{58}{-24}
=-2+5/12
$