73=5/x^2

Solution for 73=5/x^2 equation:

73=5/x^2

We move all terms to the left:

73-(5/x^2)=0


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

x!=0/1

x!=0

x∈R


We get rid of parentheses

-5/x^2+73=0

We multiply all the terms by the denominator


73*x^2-5=0

We add all the numbers together, and all the variables

73x^2-5=0

a = 73; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·73·(-5)
Δ = 1460
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1460}=\sqrt{4*365}=\sqrt{4}*\sqrt{365}=2\sqrt{365}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{365}}{2*73}=\frac{0-2\sqrt{365}}{146}
=-\frac{2\sqrt{365}}{146}
=-\frac{\sqrt{365}}{73}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{365}}{2*73}=\frac{0+2\sqrt{365}}{146}
=\frac{2\sqrt{365}}{146}
=\frac{\sqrt{365}}{73}
$