4+5x=24/x

Solution for 4+5x=24/x equation:

4+5x=24/x

We move all terms to the left:

4+5x-(24/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-(+24/x)+4=0

We get rid of parentheses

5x-24/x+4=0

We multiply all the terms by the denominator


5x*x+4*x-24=0

We add all the numbers together, and all the variables

4x+5x*x-24=0

Wy multiply elements

5x^2+4x-24=0

a = 5; b = 4; c = -24;
Δ = b2-4ac
Δ = 42-4·5·(-24)
Δ = 496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{31}}{2*5}=\frac{-4-4\sqrt{31}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{31}}{2*5}=\frac{-4+4\sqrt{31}}{10}
$