15j=3/11j

Solution for 15j=3/11j equation:

15j=3/11j

We move all terms to the left:

15j-(3/11j)=0


Domain of the equation: 11j)!=0

j!=0/1

j!=0

j∈R


We add all the numbers together, and all the variables

15j-(+3/11j)=0

We get rid of parentheses

15j-3/11j=0

We multiply all the terms by the denominator


15j*11j-3=0

Wy multiply elements

165j^2-3=0

a = 165; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·165·(-3)
Δ = 1980
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:

$\sqrt{\Delta}=\sqrt{1980}=\sqrt{36*55}=\sqrt{36}*\sqrt{55}=6\sqrt{55}$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{55}}{2*165}=\frac{0-6\sqrt{55}}{330}
=-\frac{6\sqrt{55}}{330}
=-\frac{\sqrt{55}}{55}
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{55}}{2*165}=\frac{0+6\sqrt{55}}{330}
=\frac{6\sqrt{55}}{330}
=\frac{\sqrt{55}}{55}
$