4/z+3/(2*z)=1/3

Solution for 4/z+3/(2*z)=1/3 equation:

4/z+3/(2z)=1/3

We move all terms to the left:

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


Domain of the equation: z!=0

z∈R



Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-4z^2+99z=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:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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