2/5a+3=1/3a

Solution for 2/5a+3=1/3a equation:

2/5a+3=1/3a

We move all terms to the left:

2/5a+3-(1/3a)=0


Domain of the equation: 5a!=0

a!=0/5

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

2/5a-(+1/3a)+3=0

We get rid of parentheses

2/5a-1/3a+3=0

We calculate fractions


6a/15a^2+(-5a)/15a^2+3=0

We multiply all the terms by the denominator


6a+(-5a)+3*15a^2=0

Wy multiply elements

45a^2+6a+(-5a)=0

We get rid of parentheses

45a^2+6a-5a=0

We add all the numbers together, and all the variables

45a^2+a=0

a = 45; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·45·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*45}=\frac{-2}{90}
=-1/45
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*45}=\frac{0}{90}
=0
$