24x-80=64/x

Solution for 24x-80=64/x equation:

24x-80=64/x

We move all terms to the left:

24x-80-(64/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-(+64/x)-80=0

We get rid of parentheses

24x-64/x-80=0

We multiply all the terms by the denominator


24x*x-80*x-64=0

We add all the numbers together, and all the variables

-80x+24x*x-64=0

Wy multiply elements

24x^2-80x-64=0

a = 24; b = -80; c = -64;
Δ = b2-4ac
Δ = -802-4·24·(-64)
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-112}{2*24}=\frac{-32}{48}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+112}{2*24}=\frac{192}{48}
=4
$