(4/a)+(5/3a)=3

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Solution for (4/a)+(5/3a)=3 equation:



(4/a)+(5/3a)=3
We move all terms to the left:
(4/a)+(5/3a)-(3)=0
Domain of the equation: a)!=0
a!=0/1
a!=0
a∈R
Domain of the equation: 3a)!=0
a!=0/1
a!=0
a∈R
We add all the numbers together, and all the variables
(+4/a)+(+5/3a)-3=0
We get rid of parentheses
4/a+5/3a-3=0
We calculate fractions
12a/3a^2+5a/3a^2-3=0
We multiply all the terms by the denominator
12a+5a-3*3a^2=0
We add all the numbers together, and all the variables
17a-3*3a^2=0
Wy multiply elements
-9a^2+17a=0
a = -9; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-9)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-9}=\frac{-34}{-18} =1+8/9 $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-9}=\frac{0}{-18} =0 $

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