1/6a+a=180

Solution for 1/6a+a=180 equation:

1/6a+a=180

We move all terms to the left:

1/6a+a-(180)=0


Domain of the equation: 6a!=0

a!=0/6

a!=0

a∈R


We add all the numbers together, and all the variables

a+1/6a-180=0

We multiply all the terms by the denominator


a*6a-180*6a+1=0

Wy multiply elements

6a^2-1080a+1=0

a = 6; b = -1080; c = +1;
Δ = b2-4ac
Δ = -10802-4·6·1
Δ = 1166376
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:

$\sqrt{\Delta}=\sqrt{1166376}=\sqrt{4*291594}=\sqrt{4}*\sqrt{291594}=2\sqrt{291594}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1080)-2\sqrt{291594}}{2*6}=\frac{1080-2\sqrt{291594}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1080)+2\sqrt{291594}}{2*6}=\frac{1080+2\sqrt{291594}}{12}
$