5x=24x/x

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Solution for 5x=24x/x equation: 



5x=24x/x

We move all terms to the left:

5x-(24x/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

5x-(+24x/x)=0

We get rid of parentheses

5x-24x/x=0

We multiply all the terms by the denominator


5x*x-24x=0

We add all the numbers together, and all the variables

-24x+5x*x=0

Wy multiply elements

5x^2-24x=0

a = 5; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·5·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*5}=\frac{0}{10}
=0
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*5}=\frac{48}{10}
=4+4/5
$

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