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

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∈R



Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


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
$