0=25-3/x^2

Solution for 0=25-3/x^2 equation:

0=25-3/x^2

We move all terms to the left:

0-(25-3/x^2)=0


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(25-3/x^2)=0

We get rid of parentheses

3/x^2-25=0

We multiply all the terms by the denominator


-25*x^2+3=0

We add all the numbers together, and all the variables

-25x^2+3=0

a = -25; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-25)·3
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{3}}{2*-25}=\frac{0-10\sqrt{3}}{-50}
=-\frac{10\sqrt{3}}{-50}
=-\frac{\sqrt{3}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{3}}{2*-25}=\frac{0+10\sqrt{3}}{-50}
=\frac{10\sqrt{3}}{-50}
=\frac{\sqrt{3}}{-5}
$