j-20/4j=60

Solution for j-20/4j=60 equation:

j-20/4j=60

We move all terms to the left:

j-20/4j-(60)=0


Domain of the equation: 4j!=0

j!=0/4

j!=0

j∈R


We multiply all the terms by the denominator


j*4j-60*4j-20=0

Wy multiply elements

4j^2-240j-20=0

a = 4; b = -240; c = -20;
Δ = b2-4ac
Δ = -2402-4·4·(-20)
Δ = 57920
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:

$\sqrt{\Delta}=\sqrt{57920}=\sqrt{64*905}=\sqrt{64}*\sqrt{905}=8\sqrt{905}$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-8\sqrt{905}}{2*4}=\frac{240-8\sqrt{905}}{8}
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+8\sqrt{905}}{2*4}=\frac{240+8\sqrt{905}}{8}
$