a+1/5a=180

Solution for a+1/5a=180 equation:

a+1/5a=180

We move all terms to the left:

a+1/5a-(180)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We multiply all the terms by the denominator


a*5a-180*5a+1=0

Wy multiply elements

5a^2-900a+1=0

a = 5; b = -900; c = +1;
Δ = b2-4ac
Δ = -9002-4·5·1
Δ = 809980
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:

$\sqrt{\Delta}=\sqrt{809980}=\sqrt{4*202495}=\sqrt{4}*\sqrt{202495}=2\sqrt{202495}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-2\sqrt{202495}}{2*5}=\frac{900-2\sqrt{202495}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+2\sqrt{202495}}{2*5}=\frac{900+2\sqrt{202495}}{10}
$