1/2j-16=2/3j-14

Solution for 1/2j-16=2/3j-14 equation:

1/2j-16=2/3j-14

We move all terms to the left:

1/2j-16-(2/3j-14)=0


Domain of the equation: 2j!=0

j!=0/2

j!=0

j∈R



Domain of the equation: 3j-14)!=0

j∈R


We get rid of parentheses

1/2j-2/3j+14-16=0

We calculate fractions


3j/6j^2+(-4j)/6j^2+14-16=0

We add all the numbers together, and all the variables

3j/6j^2+(-4j)/6j^2-2=0

We multiply all the terms by the denominator


3j+(-4j)-2*6j^2=0

Wy multiply elements

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

We get rid of parentheses

-12j^2+3j-4j=0

We add all the numbers together, and all the variables

-12j^2-1j=0

a = -12; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-12)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-12}=\frac{0}{-24}
=0
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-12}=\frac{2}{-24}
=-1/12
$