5/10+1/5a=1/2a

Solution for 5/10+1/5a=1/2a equation:

5/10+1/5a=1/2a

We move all terms to the left:

5/10+1/5a-(1/2a)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



Domain of the equation: 2a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

1/5a-(+1/2a)+5/10=0

We get rid of parentheses

1/5a-1/2a+5/10=0

We calculate fractions


100a^2/100a^2+20a/100a^2+(-50a)/100a^2=0

Fractions to decimals

20a/100a^2+(-50a)/100a^2+1=0

We multiply all the terms by the denominator


20a+(-50a)+1*100a^2=0

Wy multiply elements

100a^2+20a+(-50a)=0

We get rid of parentheses

100a^2+20a-50a=0

We add all the numbers together, and all the variables

100a^2-30a=0

a = 100; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·100·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*100}=\frac{0}{200}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*100}=\frac{60}{200}
=3/10
$