8/4z-3=5/9z

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Solution for 8/4z-3=5/9z equation:



8/4z-3=5/9z
We move all terms to the left:
8/4z-3-(5/9z)=0
Domain of the equation: 4z!=0
z!=0/4
z!=0
z∈R
Domain of the equation: 9z)!=0
z!=0/1
z!=0
z∈R
We add all the numbers together, and all the variables
8/4z-(+5/9z)-3=0
We get rid of parentheses
8/4z-5/9z-3=0
We calculate fractions
72z/36z^2+(-20z)/36z^2-3=0
We multiply all the terms by the denominator
72z+(-20z)-3*36z^2=0
Wy multiply elements
-108z^2+72z+(-20z)=0
We get rid of parentheses
-108z^2+72z-20z=0
We add all the numbers together, and all the variables
-108z^2+52z=0
a = -108; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·(-108)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*-108}=\frac{-104}{-216} =13/27 $
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*-108}=\frac{0}{-216} =0 $

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