1/5a+1/20a=1

Solution for 1/5a+1/20a=1 equation:

1/5a+1/20a=1

We move all terms to the left:

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


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



Domain of the equation: 20a!=0

a!=0/20

a!=0

a∈R


We calculate fractions


20a/100a^2+5a/100a^2-1=0

We multiply all the terms by the denominator


20a+5a-1*100a^2=0

We add all the numbers together, and all the variables

25a-1*100a^2=0

Wy multiply elements

-100a^2+25a=0

a = -100; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-100)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-100}=\frac{-50}{-200}
=1/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-100}=\frac{0}{-200}
=0
$