3x+1=24/x

Solution for 3x+1=24/x equation:

3x+1=24/x

We move all terms to the left:

3x+1-(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

3x-(+24/x)+1=0

We get rid of parentheses

3x-24/x+1=0

We multiply all the terms by the denominator


3x*x+1*x-24=0

We add all the numbers together, and all the variables

x+3x*x-24=0

Wy multiply elements

3x^2+x-24=0

a = 3; b = 1; c = -24;
Δ = b2-4ac
Δ = 12-4·3·(-24)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*3}=\frac{-18}{6}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*3}=\frac{16}{6}
=2+2/3
$