24/x+8=16/2x-4

Solution for 24/x+8=16/2x-4 equation:

24/x+8=16/2x-4

We move all terms to the left:

24/x+8-(16/2x-4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-4)!=0

x∈R


We get rid of parentheses

24/x-16/2x+4+8=0

We calculate fractions


48x/2x^2+(-16x)/2x^2+4+8=0

We add all the numbers together, and all the variables

48x/2x^2+(-16x)/2x^2+12=0

We multiply all the terms by the denominator


48x+(-16x)+12*2x^2=0

Wy multiply elements

24x^2+48x+(-16x)=0

We get rid of parentheses

24x^2+48x-16x=0

We add all the numbers together, and all the variables

24x^2+32x=0

a = 24; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·24·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*24}=\frac{-64}{48}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*24}=\frac{0}{48}
=0
$