1/x+1/5x=4/24

Solution for 1/x+1/5x=4/24 equation:

1/x+1/5x=4/24

We move all terms to the left:

1/x+1/5x-(4/24)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

1/x+1/5x-(+4/24)=0

We get rid of parentheses

1/x+1/5x-4/24=0

We calculate fractions


(-100x^2)/240x^2+240x/240x^2+48x/240x^2=0

We multiply all the terms by the denominator


(-100x^2)+240x+48x=0

We add all the numbers together, and all the variables

(-100x^2)+288x=0

We get rid of parentheses

-100x^2+288x=0

a = -100; b = 288; c = 0;
Δ = b2-4ac
Δ = 2882-4·(-100)·0
Δ = 82944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{82944}=288$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-288}{2*-100}=\frac{-576}{-200}
=2+22/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+288}{2*-100}=\frac{0}{-200}
=0
$