A+1/3a+a-16=180

Solution for A+1/3a+a-16=180 equation:

+1/3A+A-16=180

We move all terms to the left:

+1/3A+A-16-(180)=0


Domain of the equation: 3A!=0

A!=0/3

A!=0

A∈R


We add all the numbers together, and all the variables

A+1/3A-196=0

We multiply all the terms by the denominator


A*3A-196*3A+1=0

Wy multiply elements

3A^2-588A+1=0

a = 3; b = -588; c = +1;
Δ = b2-4ac
Δ = -5882-4·3·1
Δ = 345732
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:

$\sqrt{\Delta}=\sqrt{345732}=\sqrt{4*86433}=\sqrt{4}*\sqrt{86433}=2\sqrt{86433}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-588)-2\sqrt{86433}}{2*3}=\frac{588-2\sqrt{86433}}{6}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-588)+2\sqrt{86433}}{2*3}=\frac{588+2\sqrt{86433}}{6}
$