5/i^2=500

Solution for 5/i^2=500 equation:

5/i^2=500

We move all terms to the left:

5/i^2-(500)=0


Domain of the equation: i^2!=0

i^2!=0/

i^2!=√0

i!=0

i∈R


We multiply all the terms by the denominator


-500*i^2+5=0

We add all the numbers together, and all the variables

-500i^2+5=0

a = -500; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-500)·5
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100}{2*-500}=\frac{-100}{-1000}
=1/10
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100}{2*-500}=\frac{100}{-1000}
=-1/10
$