5=10^4/y^2

Solution for 5=10^4/y^2 equation:

5=10^4/y^2

We move all terms to the left:

5-(10^4/y^2)=0


Domain of the equation: y^2)!=0

y!=0/1

y!=0

y∈R


We get rid of parentheses

-10^4/y^2+5=0

We multiply all the terms by the denominator


5*y^2-10^4=0

We add all the numbers together, and all the variables

5y^2-10000=0

a = 5; b = 0; c = -10000;
Δ = b2-4ac
Δ = 02-4·5·(-10000)
Δ = 200000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{200000}=\sqrt{40000*5}=\sqrt{40000}*\sqrt{5}=200\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{5}}{2*5}=\frac{0-200\sqrt{5}}{10}
=-\frac{200\sqrt{5}}{10}
=-20\sqrt{5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{5}}{2*5}=\frac{0+200\sqrt{5}}{10}
=\frac{200\sqrt{5}}{10}
=20\sqrt{5}
$