1/x+1/2x=1/12

Solution for 1/x+1/2x=1/12 equation:

1/x+1/2x=1/12

We move all terms to the left:

1/x+1/2x-(1/12)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/x+1/2x-(+1/12)=0

We get rid of parentheses

1/x+1/2x-1/12=0

We calculate fractions


(-4x^2)/24x^2+24x/24x^2+12x/24x^2=0

We multiply all the terms by the denominator


(-4x^2)+24x+12x=0

We add all the numbers together, and all the variables

(-4x^2)+36x=0

We get rid of parentheses

-4x^2+36x=0

a = -4; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-4)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-4}=\frac{-72}{-8}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-4}=\frac{0}{-8}
=0
$