4*1/6z=-2+5*2/3z

Solution for 4*1/6z=-2+5*2/3z equation:

4*1/6z=-2+5*2/3z

We move all terms to the left:

4*1/6z-(-2+5*2/3z)=0


Domain of the equation: 6z!=0

z!=0/6

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

4*1/6z-(5*2/3z-2)=0

We get rid of parentheses

4*1/6z-5*2/3z+2=0

We calculate fractions


36z/18z^2+(-360z)/18z^2+2=0

We multiply all the terms by the denominator


36z+(-360z)+2*18z^2=0

Wy multiply elements

36z^2+36z+(-360z)=0

We get rid of parentheses

36z^2+36z-360z=0

We add all the numbers together, and all the variables

36z^2-324z=0

a = 36; b = -324; c = 0;
Δ = b2-4ac
Δ = -3242-4·36·0
Δ = 104976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{104976}=324$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-324)-324}{2*36}=\frac{0}{72}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-324)+324}{2*36}=\frac{648}{72}
=9
$