1/5a+4/5a=a

Solution for 1/5a+4/5a=a equation:

1/5a+4/5a=a

We move all terms to the left:

1/5a+4/5a-(a)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We add all the numbers together, and all the variables

-1a+1/5a+4/5a=0

We multiply all the terms by the denominator


-1a*5a+1+4=0

We add all the numbers together, and all the variables

-1a*5a+5=0

Wy multiply elements

-5a^2+5=0

a = -5; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-5)·5
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10}{2*-5}=\frac{-10}{-10}
=1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10}{2*-5}=\frac{10}{-10}
=-1
$