x/3x-4=2x+3

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

x/3x-4=2x+3

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2+x-9x-12x=0

We add all the numbers together, and all the variables

-6x^2-20x=0

a = -6; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-6)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-6}=\frac{40}{-12}
=-3+1/3
$