3a+1/a=21

Solution for 3a+1/a=21 equation:

3a+1/a=21

We move all terms to the left:

3a+1/a-(21)=0


Domain of the equation: a!=0

a∈R


We multiply all the terms by the denominator


3a*a-21*a+1=0

We add all the numbers together, and all the variables

-21a+3a*a+1=0

Wy multiply elements

3a^2-21a+1=0

a = 3; b = -21; c = +1;
Δ = b2-4ac
Δ = -212-4·3·1
Δ = 429
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{429}}{2*3}=\frac{21-\sqrt{429}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{429}}{2*3}=\frac{21+\sqrt{429}}{6}
$