1/4j+18=j

Solution for 1/4j+18=j equation:

1/4j+18=j

We move all terms to the left:

1/4j+18-(j)=0


Domain of the equation: 4j!=0

j!=0/4

j!=0

j∈R


We add all the numbers together, and all the variables

-1j+1/4j+18=0

We multiply all the terms by the denominator


-1j*4j+18*4j+1=0

Wy multiply elements

-4j^2+72j+1=0

a = -4; b = 72; c = +1;
Δ = b2-4ac
Δ = 722-4·(-4)·1
Δ = 5200
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:

$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-20\sqrt{13}}{2*-4}=\frac{-72-20\sqrt{13}}{-8}
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+20\sqrt{13}}{2*-4}=\frac{-72+20\sqrt{13}}{-8}
$