j-6=1/j+3

Solution for j-6=1/j+3 equation:

j-6=1/j+3

We move all terms to the left:

j-6-(1/j+3)=0


Domain of the equation: j+3)!=0

j∈R


We get rid of parentheses

j-1/j-3-6=0

We multiply all the terms by the denominator


j*j-3*j-6*j-1=0

We add all the numbers together, and all the variables

-9j+j*j-1=0

Wy multiply elements

j^2-9j-1=0

a = 1; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·1·(-1)
Δ = 85
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{85}}{2*1}=\frac{9-\sqrt{85}}{2}
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{85}}{2*1}=\frac{9+\sqrt{85}}{2}
$