24/x=64/2x+2

Solution for 24/x=64/2x+2 equation:

24/x=64/2x+2

We move all terms to the left:

24/x-(64/2x+2)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

24/x-64/2x-2=0

We calculate fractions


48x/2x^2+(-64x)/2x^2-2=0

We multiply all the terms by the denominator


48x+(-64x)-2*2x^2=0

Wy multiply elements

-4x^2+48x+(-64x)=0

We get rid of parentheses

-4x^2+48x-64x=0

We add all the numbers together, and all the variables

-4x^2-16x=0

a = -4; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-4)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-4}=\frac{32}{-8}
=-4
$