a+1/3a=180

Solution for a+1/3a=180 equation:

a+1/3a=180

We move all terms to the left:

a+1/3a-(180)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We multiply all the terms by the denominator


a*3a-180*3a+1=0

Wy multiply elements

3a^2-540a+1=0

a = 3; b = -540; c = +1;
Δ = b2-4ac
Δ = -5402-4·3·1
Δ = 291588
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:

$\sqrt{\Delta}=\sqrt{291588}=\sqrt{8836*33}=\sqrt{8836}*\sqrt{33}=94\sqrt{33}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-94\sqrt{33}}{2*3}=\frac{540-94\sqrt{33}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+94\sqrt{33}}{2*3}=\frac{540+94\sqrt{33}}{6}
$