20=225/x^2

Solution for 20=225/x^2 equation:

20=225/x^2

We move all terms to the left:

20-(225/x^2)=0


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

x!=0/1

x!=0

x∈R


We get rid of parentheses

-225/x^2+20=0

We multiply all the terms by the denominator


20*x^2-225=0

We add all the numbers together, and all the variables

20x^2-225=0

a = 20; b = 0; c = -225;
Δ = b2-4ac
Δ = 02-4·20·(-225)
Δ = 18000
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:

$\sqrt{\Delta}=\sqrt{18000}=\sqrt{3600*5}=\sqrt{3600}*\sqrt{5}=60\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{5}}{2*20}=\frac{0-60\sqrt{5}}{40}
=-\frac{60\sqrt{5}}{40}
=-\frac{3\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{5}}{2*20}=\frac{0+60\sqrt{5}}{40}
=\frac{60\sqrt{5}}{40}
=\frac{3\sqrt{5}}{2}
$