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

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

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

We move all terms to the left:

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


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R



Domain of the equation: 4z-4)!=0

z∈R


We get rid of parentheses

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

We calculate fractions


12z/8z^2+10z/8z^2+4-2=0

We add all the numbers together, and all the variables

12z/8z^2+10z/8z^2+2=0

We multiply all the terms by the denominator


12z+10z+2*8z^2=0

We add all the numbers together, and all the variables

22z+2*8z^2=0

Wy multiply elements

16z^2+22z=0

a = 16; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·16·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*16}=\frac{-44}{32}
=-1+3/8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*16}=\frac{0}{32}
=0
$