a+1/3a=20

Solution for a+1/3a=20 equation:

a+1/3a=20

We move all terms to the left:

a+1/3a-(20)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We multiply all the terms by the denominator


a*3a-20*3a+1=0

Wy multiply elements

3a^2-60a+1=0

a = 3; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·3·1
Δ = 3588
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3588}=\sqrt{4*897}=\sqrt{4}*\sqrt{897}=2\sqrt{897}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{897}}{2*3}=\frac{60-2\sqrt{897}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{897}}{2*3}=\frac{60+2\sqrt{897}}{6}
$