1/x+1/2x=1/22

Solution for 1/x+1/2x=1/22 equation:

1/x+1/2x=1/22

We move all terms to the left:

1/x+1/2x-(1/22)=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-(+1/22)=0

We get rid of parentheses

1/x+1/2x-1/22=0

We calculate fractions


(-4x^2)/88x^2+88x/88x^2+44x/88x^2=0

We multiply all the terms by the denominator


(-4x^2)+88x+44x=0

We add all the numbers together, and all the variables

(-4x^2)+132x=0

We get rid of parentheses

-4x^2+132x=0

a = -4; b = 132; c = 0;
Δ = b2-4ac
Δ = 1322-4·(-4)·0
Δ = 17424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17424}=132$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(132)-132}{2*-4}=\frac{-264}{-8}
=+33
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(132)+132}{2*-4}=\frac{0}{-8}
=0
$