1/a-3/5a=2

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

1/a-3/5a=2

We move all terms to the left:

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


Domain of the equation: a!=0

a∈R



Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-10a^2+5a+(-3a)=0

We get rid of parentheses

-10a^2+5a-3a=0

We add all the numbers together, and all the variables

-10a^2+2a=0

a = -10; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-10)·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*-10}=\frac{-4}{-20}
=1/5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-10}=\frac{0}{-20}
=0
$