1/a+1/3a+8=22

Solution for 1/a+1/3a+8=22 equation:

1/a+1/3a+8=22

We move all terms to the left:

1/a+1/3a+8-(22)=0


Domain of the equation: a!=0

a∈R



Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We add all the numbers together, and all the variables

1/a+1/3a-14=0

We calculate fractions


3a/3a^2+a/3a^2-14=0

We multiply all the terms by the denominator


3a+a-14*3a^2=0

We add all the numbers together, and all the variables

4a-14*3a^2=0

Wy multiply elements

-42a^2+4a=0

a = -42; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-42)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-42}=\frac{-8}{-84}
=2/21
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-42}=\frac{0}{-84}
=0
$