1/3a-20=1/5a

Solution for 1/3a-20=1/5a equation:

1/3a-20=1/5a

We move all terms to the left:

1/3a-20-(1/5a)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 5a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

1/3a-(+1/5a)-20=0

We get rid of parentheses

1/3a-1/5a-20=0

We calculate fractions


5a/15a^2+(-3a)/15a^2-20=0

We multiply all the terms by the denominator


5a+(-3a)-20*15a^2=0

Wy multiply elements

-300a^2+5a+(-3a)=0

We get rid of parentheses

-300a^2+5a-3a=0

We add all the numbers together, and all the variables

-300a^2+2a=0

a = -300; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-300)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-300}=\frac{-4}{-600}
=1/150
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-300}=\frac{0}{-600}
=0
$