4/x+3/2x=1/3

Solution for 4/x+3/2x=1/3 equation:

4/x+3/2x=1/3

We move all terms to the left:

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

We get rid of parentheses

4/x+3/2x-1/3=0

We calculate fractions


(-4x^2)/18x^2+72x/18x^2+27x/18x^2=0

We multiply all the terms by the denominator


(-4x^2)+72x+27x=0

We add all the numbers together, and all the variables

(-4x^2)+99x=0

We get rid of parentheses

-4x^2+99x=0

a = -4; b = 99; c = 0;
Δ = b2-4ac
Δ = 992-4·(-4)·0
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(99)-99}{2*-4}=\frac{-198}{-8}
=24+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(99)+99}{2*-4}=\frac{0}{-8}
=0
$