3/2z-1=3-2/3z

Solution for 3/2z-1=3-2/3z equation:

3/2z-1=3-2/3z

We move all terms to the left:

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


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R



Domain of the equation: 3z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


9z/6z^2+4z/6z^2-3-1=0

We add all the numbers together, and all the variables

9z/6z^2+4z/6z^2-4=0

We multiply all the terms by the denominator


9z+4z-4*6z^2=0

We add all the numbers together, and all the variables

13z-4*6z^2=0

Wy multiply elements

-24z^2+13z=0

a = -24; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-24)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-24}=\frac{-26}{-48}
=13/24
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-24}=\frac{0}{-48}
=0
$