24x^-1=24/x

Solution for 24x^-1=24/x equation:

24x^-1=24/x

We move all terms to the left:

24x^-1-(24/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

24x^-(+24/x)-1=0

We add all the numbers together, and all the variables

24x-(+24/x)-1=0

We get rid of parentheses

24x-24/x-1=0

We multiply all the terms by the denominator


24x*x-1*x-24=0

We add all the numbers together, and all the variables

-1x+24x*x-24=0

Wy multiply elements

24x^2-1x-24=0

a = 24; b = -1; c = -24;
Δ = b2-4ac
Δ = -12-4·24·(-24)
Δ = 2305
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{2305}}{2*24}=\frac{1-\sqrt{2305}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{2305}}{2*24}=\frac{1+\sqrt{2305}}{48}
$