3x/1x+24=1/x

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

3x/1x+24=1/x

We move all terms to the left:

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


Domain of the equation: 1x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


3x^2/x^2+(-x)/x^2+24=0

We add all the numbers together, and all the variables

3x^2/x^2+(-1x)/x^2+24=0

We multiply all the terms by the denominator


3x^2+(-1x)+24*x^2=0

We add all the numbers together, and all the variables

27x^2+(-1x)=0

We get rid of parentheses

27x^2-1x=0

a = 27; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·27·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*27}=\frac{0}{54}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*27}=\frac{2}{54}
=1/27
$