-(1/2)j=-3

Solution for -(1/2)j=-3 equation:

-(1/2)j=-3

We move all terms to the left:

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


Domain of the equation: 2)j!=0

j!=0/1

j!=0

j∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-j^2+3=0

We add all the numbers together, and all the variables

-1j^2+3=0

a = -1; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-1)·3
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3}}{2*-1}=\frac{0-2\sqrt{3}}{-2}
=-\frac{2\sqrt{3}}{-2}
=-\frac{\sqrt{3}}{-1}
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3}}{2*-1}=\frac{0+2\sqrt{3}}{-2}
=\frac{2\sqrt{3}}{-2}
=\frac{\sqrt{3}}{-1}
$