1/x+1/2x=3/14

Solution for 1/x+1/2x=3/14 equation:

1/x+1/2x=3/14

We move all terms to the left:

1/x+1/2x-(3/14)=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-(+3/14)=0

We get rid of parentheses

1/x+1/2x-3/14=0

We calculate fractions


(-12x^2)/28x^2+28x/28x^2+14x/28x^2=0

We multiply all the terms by the denominator


(-12x^2)+28x+14x=0

We add all the numbers together, and all the variables

(-12x^2)+42x=0

We get rid of parentheses

-12x^2+42x=0

a = -12; b = 42; c = 0;
Δ = b2-4ac
Δ = 422-4·(-12)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-42}{2*-12}=\frac{-84}{-24}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42}{2*-12}=\frac{0}{-24}
=0
$