1/3z-3=5-3/2z

Solution for 1/3z-3=5-3/2z equation:

1/3z-3=5-3/2z

We move all terms to the left:

1/3z-3-(5-3/2z)=0


Domain of the equation: 3z!=0

z!=0/3

z!=0

z∈R



Domain of the equation: 2z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

1/3z-(-3/2z+5)-3=0

We get rid of parentheses

1/3z+3/2z-5-3=0

We calculate fractions


2z/6z^2+9z/6z^2-5-3=0

We add all the numbers together, and all the variables

2z/6z^2+9z/6z^2-8=0

We multiply all the terms by the denominator


2z+9z-8*6z^2=0

We add all the numbers together, and all the variables

11z-8*6z^2=0

Wy multiply elements

-48z^2+11z=0

a = -48; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-48)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-48}=\frac{-22}{-96}
=11/48
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-48}=\frac{0}{-96}
=0
$