2/8+1/4a=1/2a

Solution for 2/8+1/4a=1/2a equation:

2/8+1/4a=1/2a

We move all terms to the left:

2/8+1/4a-(1/2a)=0


Domain of the equation: 4a!=0

a!=0/4

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

1/4a-(+1/2a)+2/8=0

We get rid of parentheses

1/4a-1/2a+2/8=0

We calculate fractions


32a^2/512a^2+128a/512a^2+(-256a)/512a^2=0

We multiply all the terms by the denominator


32a^2+128a+(-256a)=0

We get rid of parentheses

32a^2+128a-256a=0

We add all the numbers together, and all the variables

32a^2-128a=0

a = 32; b = -128; c = 0;
Δ = b2-4ac
Δ = -1282-4·32·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-128}{2*32}=\frac{0}{64}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+128}{2*32}=\frac{256}{64}
=4
$