1/a+2=8/3a+1

Solution for 1/a+2=8/3a+1 equation:

1/a+2=8/3a+1

We move all terms to the left:

1/a+2-(8/3a+1)=0


Domain of the equation: a!=0

a∈R



Domain of the equation: 3a+1)!=0

a∈R


We get rid of parentheses

1/a-8/3a-1+2=0

We calculate fractions


3a/3a^2+(-8a)/3a^2-1+2=0

We add all the numbers together, and all the variables

3a/3a^2+(-8a)/3a^2+1=0

We multiply all the terms by the denominator


3a+(-8a)+1*3a^2=0

Wy multiply elements

3a^2+3a+(-8a)=0

We get rid of parentheses

3a^2+3a-8a=0

We add all the numbers together, and all the variables

3a^2-5a=0

a = 3; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·3·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*3}=\frac{0}{6}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*3}=\frac{10}{6}
=1+2/3
$