2a+1/2a=180

Solution for 2a+1/2a=180 equation:

2a+1/2a=180

We move all terms to the left:

2a+1/2a-(180)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We multiply all the terms by the denominator


2a*2a-180*2a+1=0

Wy multiply elements

4a^2-360a+1=0

a = 4; b = -360; c = +1;
Δ = b2-4ac
Δ = -3602-4·4·1
Δ = 129584
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:

$\sqrt{\Delta}=\sqrt{129584}=\sqrt{16*8099}=\sqrt{16}*\sqrt{8099}=4\sqrt{8099}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-4\sqrt{8099}}{2*4}=\frac{360-4\sqrt{8099}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+4\sqrt{8099}}{2*4}=\frac{360+4\sqrt{8099}}{8}
$