60/j=12,j=

Solution for 60/j=12,j= equation:

60/j=12.j=

We move all terms to the left:

60/j-(12.j)=0


Domain of the equation: j!=0

j∈R


We add all the numbers together, and all the variables

60/j-(+12.j)=0

We get rid of parentheses

60/j-12.j=0

We multiply all the terms by the denominator


-(12.j)*j+60=0

We add all the numbers together, and all the variables

-(+12.j)*j+60=0

We multiply parentheses

-12j^2+60=0

a = -12; b = 0; c = +60;
Δ = b2-4ac
Δ = 02-4·(-12)·60
Δ = 2880
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:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{5}}{2*-12}=\frac{0-24\sqrt{5}}{-24}
=-\frac{24\sqrt{5}}{-24}
=-\frac{\sqrt{5}}{-1}
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{5}}{2*-12}=\frac{0+24\sqrt{5}}{-24}
=\frac{24\sqrt{5}}{-24}
=\frac{\sqrt{5}}{-1}
$