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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


36x^2/144x^2+96x/144x^2+(-60x)/144x^2=0

We multiply all the terms by the denominator


36x^2+96x+(-60x)=0

We get rid of parentheses

36x^2+96x-60x=0

We add all the numbers together, and all the variables

36x^2+36x=0

a = 36; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·36·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*36}=\frac{-72}{72}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*36}=\frac{0}{72}
=0
$