1/x+1/2x+3/x=11

Solution for 1/x+1/2x+3/x=11 equation:

1/x+1/2x+3/x=11

We move all terms to the left:

1/x+1/2x+3/x-(11)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


(6x+1)/2x^2+x/2x^2-11=0

We multiply all the terms by the denominator


(6x+1)+x-11*2x^2=0

We add all the numbers together, and all the variables

x+(6x+1)-11*2x^2=0

Wy multiply elements

-22x^2+x+(6x+1)=0

We get rid of parentheses

-22x^2+x+6x+1=0

We add all the numbers together, and all the variables

-22x^2+7x+1=0

a = -22; b = 7; c = +1;
Δ = b2-4ac
Δ = 72-4·(-22)·1
Δ = 137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{137}}{2*-22}=\frac{-7-\sqrt{137}}{-44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{137}}{2*-22}=\frac{-7+\sqrt{137}}{-44}
$