5/2z=2-4/3z

Solution for 5/2z=2-4/3z equation:

5/2z=2-4/3z

We move all terms to the left:

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

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

We get rid of parentheses

5/2z+4/3z-2=0

We calculate fractions


15z/6z^2+8z/6z^2-2=0

We multiply all the terms by the denominator


15z+8z-2*6z^2=0

We add all the numbers together, and all the variables

23z-2*6z^2=0

Wy multiply elements

-12z^2+23z=0

a = -12; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-12)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-12}=\frac{-46}{-24}
=1+11/12
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-12}=\frac{0}{-24}
=0
$