24=4x+32/x

Solution for 24=4x+32/x equation:

24=4x+32/x

We move all terms to the left:

24-(4x+32/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

-(+4x+32/x)+24=0

We get rid of parentheses

-4x-32/x+24=0

We multiply all the terms by the denominator


-4x*x+24*x-32=0

We add all the numbers together, and all the variables

24x-4x*x-32=0

Wy multiply elements

-4x^2+24x-32=0

a = -4; b = 24; c = -32;
Δ = b2-4ac
Δ = 242-4·(-4)·(-32)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8}{2*-4}=\frac{-32}{-8}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8}{2*-4}=\frac{-16}{-8}
=+2
$