2/3j-1/2=3/4j=1/3

Solution for 2/3j-1/2=3/4j=1/3 equation:

2/3j-1/2=3/4j=1/3

We move all terms to the left:

2/3j-1/2-(3/4j)=0


Domain of the equation: 3j!=0

j!=0/3

j!=0

j∈R



Domain of the equation: 4j)!=0

j!=0/1

j!=0

j∈R


We add all the numbers together, and all the variables

2/3j-(+3/4j)-1/2=0

We get rid of parentheses

2/3j-3/4j-1/2=0

We calculate fractions


(-48j^2)/48j^2+32j/48j^2+(-36j)/48j^2=0

We multiply all the terms by the denominator


(-48j^2)+32j+(-36j)=0

We get rid of parentheses

-48j^2+32j-36j=0

We add all the numbers together, and all the variables

-48j^2-4j=0

a = -48; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-48)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-48}=\frac{0}{-96}
=0
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-48}=\frac{8}{-96}
=-1/12
$