a+2/3a=180

Solution for a+2/3a=180 equation:

a+2/3a=180

We move all terms to the left:

a+2/3a-(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+2=0

Wy multiply elements

3a^2-540a+2=0

a = 3; b = -540; c = +2;
Δ = b2-4ac
Δ = -5402-4·3·2
Δ = 291576
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:

$\sqrt{\Delta}=\sqrt{291576}=\sqrt{4*72894}=\sqrt{4}*\sqrt{72894}=2\sqrt{72894}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-2\sqrt{72894}}{2*3}=\frac{540-2\sqrt{72894}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+2\sqrt{72894}}{2*3}=\frac{540+2\sqrt{72894}}{6}
$