j-9/5j=4

Solution for j-9/5j=4 equation:

j-9/5j=4

We move all terms to the left:

j-9/5j-(4)=0


Domain of the equation: 5j!=0

j!=0/5

j!=0

j∈R


We multiply all the terms by the denominator


j*5j-4*5j-9=0

Wy multiply elements

5j^2-20j-9=0

a = 5; b = -20; c = -9;
Δ = b2-4ac
Δ = -202-4·5·(-9)
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{145}}{2*5}=\frac{20-2\sqrt{145}}{10}
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{145}}{2*5}=\frac{20+2\sqrt{145}}{10}
$