4/x+2/2x=11/6

Solution for 4/x+2/2x=11/6 equation:

4/x+2/2x=11/6

We move all terms to the left:

4/x+2/2x-(11/6)=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

4/x+2/2x-(+11/6)=0

We get rid of parentheses

4/x+2/2x-11/6=0

We calculate fractions


(-44x^2)/72x^2+288x/72x^2+72x/72x^2=0

We multiply all the terms by the denominator


(-44x^2)+288x+72x=0

We add all the numbers together, and all the variables

(-44x^2)+360x=0

We get rid of parentheses

-44x^2+360x=0

a = -44; b = 360; c = 0;
Δ = b2-4ac
Δ = 3602-4·(-44)·0
Δ = 129600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{129600}=360$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-360}{2*-44}=\frac{-720}{-88}
=8+2/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+360}{2*-44}=\frac{0}{-88}
=0
$