a+31/2a=180

Solution for a+31/2a=180 equation:

a+31/2a=180

We move all terms to the left:

a+31/2a-(180)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We multiply all the terms by the denominator


a*2a-180*2a+31=0

Wy multiply elements

2a^2-360a+31=0

a = 2; b = -360; c = +31;
Δ = b2-4ac
Δ = -3602-4·2·31
Δ = 129352
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:

$\sqrt{\Delta}=\sqrt{129352}=\sqrt{4*32338}=\sqrt{4}*\sqrt{32338}=2\sqrt{32338}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-2\sqrt{32338}}{2*2}=\frac{360-2\sqrt{32338}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+2\sqrt{32338}}{2*2}=\frac{360+2\sqrt{32338}}{4}
$