j+1/3j+1/3j=50-15

Solution for j+1/3j+1/3j=50-15 equation:

j+1/3j+1/3j=50-15

We move all terms to the left:

j+1/3j+1/3j-(50-15)=0


Domain of the equation: 3j!=0

j!=0/3

j!=0

j∈R


We add all the numbers together, and all the variables

j+1/3j+1/3j-35=0

We multiply all the terms by the denominator


j*3j-35*3j+1+1=0

We add all the numbers together, and all the variables

j*3j-35*3j+2=0

Wy multiply elements

3j^2-105j+2=0

a = 3; b = -105; c = +2;
Δ = b2-4ac
Δ = -1052-4·3·2
Δ = 11001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-\sqrt{11001}}{2*3}=\frac{105-\sqrt{11001}}{6}
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{11001}}{2*3}=\frac{105+\sqrt{11001}}{6}
$