2/x+1/3x=7/6

Solution for 2/x+1/3x=7/6 equation:

2/x+1/3x=7/6

We move all terms to the left:

2/x+1/3x-(7/6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/x+1/3x-(+7/6)=0

We get rid of parentheses

2/x+1/3x-7/6=0

We calculate fractions


(-63x^2)/108x^2+216x/108x^2+36x/108x^2=0

We multiply all the terms by the denominator


(-63x^2)+216x+36x=0

We add all the numbers together, and all the variables

(-63x^2)+252x=0

We get rid of parentheses

-63x^2+252x=0

a = -63; b = 252; c = 0;
Δ = b2-4ac
Δ = 2522-4·(-63)·0
Δ = 63504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63504}=252$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(252)-252}{2*-63}=\frac{-504}{-126}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+252}{2*-63}=\frac{0}{-126}
=0
$