24=90/x^2

Solution for 24=90/x^2 equation:

24=90/x^2

We move all terms to the left:

24-(90/x^2)=0


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

x!=0/1

x!=0

x∈R


We get rid of parentheses

-90/x^2+24=0

We multiply all the terms by the denominator


24*x^2-90=0

We add all the numbers together, and all the variables

24x^2-90=0

a = 24; b = 0; c = -90;
Δ = b2-4ac
Δ = 02-4·24·(-90)
Δ = 8640
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:

$\sqrt{\Delta}=\sqrt{8640}=\sqrt{576*15}=\sqrt{576}*\sqrt{15}=24\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{15}}{2*24}=\frac{0-24\sqrt{15}}{48}
=-\frac{24\sqrt{15}}{48}
=-\frac{\sqrt{15}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{15}}{2*24}=\frac{0+24\sqrt{15}}{48}
=\frac{24\sqrt{15}}{48}
=\frac{\sqrt{15}}{2}
$