2/3j-1/6j=-4

Solution for 2/3j-1/6j=-4 equation:

2/3j-1/6j=-4

We move all terms to the left:

2/3j-1/6j-(-4)=0


Domain of the equation: 3j!=0

j!=0/3

j!=0

j∈R



Domain of the equation: 6j!=0

j!=0/6

j!=0

j∈R


We add all the numbers together, and all the variables

2/3j-1/6j+4=0

We calculate fractions


12j/18j^2+(-3j)/18j^2+4=0

We multiply all the terms by the denominator


12j+(-3j)+4*18j^2=0

Wy multiply elements

72j^2+12j+(-3j)=0

We get rid of parentheses

72j^2+12j-3j=0

We add all the numbers together, and all the variables

72j^2+9j=0

a = 72; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·72·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*72}=\frac{-18}{144}
=-1/8
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*72}=\frac{0}{144}
=0
$