4/a-1/5a=3

Solution for 4/a-1/5a=3 equation:

4/a-1/5a=3

We move all terms to the left:

4/a-1/5a-(3)=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


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

We add all the numbers together, and all the variables

20a/5a^2+(-1a)/5a^2-3=0

We multiply all the terms by the denominator


20a+(-1a)-3*5a^2=0

Wy multiply elements

-15a^2+20a+(-1a)=0

We get rid of parentheses

-15a^2+20a-1a=0

We add all the numbers together, and all the variables

-15a^2+19a=0

a = -15; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-15)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-15}=\frac{-38}{-30}
=1+4/15
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-15}=\frac{0}{-30}
=0
$