5/4z+3/2z=1

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

5/4z+3/2z=1

We move all terms to the left:

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


Domain of the equation: 4z!=0

z!=0/4

z!=0

z∈R



Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


We calculate fractions


10z/8z^2+12z/8z^2-1=0

We multiply all the terms by the denominator


10z+12z-1*8z^2=0

We add all the numbers together, and all the variables

22z-1*8z^2=0

Wy multiply elements

-8z^2+22z=0

a = -8; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-8)·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*-8}=\frac{-44}{-16}
=2+3/4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-8}=\frac{0}{-16}
=0
$