2/3j+8-1/4j=12

Solution for 2/3j+8-1/4j=12 equation:

2/3j+8-1/4j=12

We move all terms to the left:

2/3j+8-1/4j-(12)=0


Domain of the equation: 3j!=0

j!=0/3

j!=0

j∈R



Domain of the equation: 4j!=0

j!=0/4

j!=0

j∈R


We add all the numbers together, and all the variables

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

We calculate fractions


8j/12j^2+(-3j)/12j^2-4=0

We multiply all the terms by the denominator


8j+(-3j)-4*12j^2=0

Wy multiply elements

-48j^2+8j+(-3j)=0

We get rid of parentheses

-48j^2+8j-3j=0

We add all the numbers together, and all the variables

-48j^2+5j=0

a = -48; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-48)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-48}=\frac{-10}{-96}
=5/48
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-48}=\frac{0}{-96}
=0
$