2/x+3/2x=5/6

Solution for 2/x+3/2x=5/6 equation:

2/x+3/2x=5/6

We move all terms to the left:

2/x+3/2x-(5/6)=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

2/x+3/2x-(+5/6)=0

We get rid of parentheses

2/x+3/2x-5/6=0

We calculate fractions


(-20x^2)/72x^2+144x/72x^2+108x/72x^2=0

We multiply all the terms by the denominator


(-20x^2)+144x+108x=0

We add all the numbers together, and all the variables

(-20x^2)+252x=0

We get rid of parentheses

-20x^2+252x=0

a = -20; b = 252; c = 0;
Δ = b2-4ac
Δ = 2522-4·(-20)·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*-20}=\frac{-504}{-40}
=12+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+252}{2*-20}=\frac{0}{-40}
=0
$