1/x+1/3x=1/60

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Solution for 1/x+1/3x=1/60 equation: 



1/x+1/3x=1/60

We move all terms to the left:

1/x+1/3x-(1/60)=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-(+1/60)=0

We get rid of parentheses

1/x+1/3x-1/60=0

We calculate fractions


(-9x^2)/1080x^2+1080x/1080x^2+360x/1080x^2=0

We multiply all the terms by the denominator


(-9x^2)+1080x+360x=0

We add all the numbers together, and all the variables

(-9x^2)+1440x=0

We get rid of parentheses

-9x^2+1440x=0

a = -9; b = 1440; c = 0;
Δ = b2-4ac
Δ = 14402-4·(-9)·0
Δ = 2073600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2073600}=1440$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1440)-1440}{2*-9}=\frac{-2880}{-18}
=+160
$


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

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