5/12x-3=2/3x+1

Solution for 5/12x-3=2/3x+1 equation:

5/12x-3=2/3x+1

We move all terms to the left:

5/12x-3-(2/3x+1)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 3x+1)!=0

x∈R


We get rid of parentheses

5/12x-2/3x-1-3=0

We calculate fractions


15x/36x^2+(-24x)/36x^2-1-3=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-144x^2+15x+(-24x)=0

We get rid of parentheses

-144x^2+15x-24x=0

We add all the numbers together, and all the variables

-144x^2-9x=0

a = -144; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-144)·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*-144}=\frac{0}{-288}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-144}=\frac{18}{-288}
=-1/16
$