24/x=8,x

Solution for 24/x=8,x equation:

24/x=8.x

We move all terms to the left:

24/x-(8.x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

24/x-(+8.x)=0

We get rid of parentheses

24/x-8.x=0

We multiply all the terms by the denominator


-(8.x)*x+24=0

We add all the numbers together, and all the variables

-(+8.x)*x+24=0

We multiply parentheses

-8x^2+24=0

a = -8; b = 0; c = +24;
Δ = b2-4ac
Δ = 02-4·(-8)·24
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{3}}{2*-8}=\frac{0-16\sqrt{3}}{-16}
=-\frac{16\sqrt{3}}{-16}
=-\frac{\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{3}}{2*-8}=\frac{0+16\sqrt{3}}{-16}
=\frac{16\sqrt{3}}{-16}
=\frac{\sqrt{3}}{-1}
$