1/x+1/3x=1/45

Solution for 1/x+1/3x=1/45 equation:

1/x+1/3x=1/45

We move all terms to the left:

1/x+1/3x-(1/45)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/x+1/3x-(+1/45)=0

We get rid of parentheses

1/x+1/3x-1/45=0

We calculate fractions


(-9x^2)/540x^2+540x/540x^2+180x/540x^2=0

We multiply all the terms by the denominator


(-9x^2)+540x+180x=0

We add all the numbers together, and all the variables

(-9x^2)+720x=0

We get rid of parentheses

-9x^2+720x=0

a = -9; b = 720; c = 0;
Δ = b2-4ac
Δ = 7202-4·(-9)·0
Δ = 518400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{518400}=720$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(720)-720}{2*-9}=\frac{-1440}{-18}
=+80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(720)+720}{2*-9}=\frac{0}{-18}
=0
$