5/12x+2=2/3x-4

Solution for 5/12x+2=2/3x-4 equation:

5/12x+2=2/3x-4

We move all terms to the left:

5/12x+2-(2/3x-4)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

5/12x-2/3x+4+2=0

We calculate fractions


15x/36x^2+(-24x)/36x^2+4+2=0

We add all the numbers together, and all the variables

15x/36x^2+(-24x)/36x^2+6=0

We multiply all the terms by the denominator


15x+(-24x)+6*36x^2=0

Wy multiply elements

216x^2+15x+(-24x)=0

We get rid of parentheses

216x^2+15x-24x=0

We add all the numbers together, and all the variables

216x^2-9x=0

a = 216; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·216·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*216}=\frac{0}{432}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*216}=\frac{18}{432}
=1/24
$