3/2z=5(4z)

Solution for 3/2z=5(4z) equation:

3/2z=5(4z)

We move all terms to the left:

3/2z-(5(4z))=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


determiningTheFunctionDomain
3/2z-54z=0

We add all the numbers together, and all the variables

-54z+3/2z=0

We multiply all the terms by the denominator


-54z*2z+3=0

Wy multiply elements

-108z^2+3=0

a = -108; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-108)·3
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36}{2*-108}=\frac{-36}{-216}
=1/6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36}{2*-108}=\frac{36}{-216}
=-1/6
$