a=41/2a

Solution for a=41/2a equation:

a=41/2a

We move all terms to the left:

a-(41/2a)=0


Domain of the equation: 2a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

a-(+41/2a)=0

We get rid of parentheses

a-41/2a=0

We multiply all the terms by the denominator


a*2a-41=0

Wy multiply elements

2a^2-41=0

a = 2; b = 0; c = -41;
Δ = b2-4ac
Δ = 02-4·2·(-41)
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{82}}{2*2}=\frac{0-2\sqrt{82}}{4}
=-\frac{2\sqrt{82}}{4}
=-\frac{\sqrt{82}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{82}}{2*2}=\frac{0+2\sqrt{82}}{4}
=\frac{2\sqrt{82}}{4}
=\frac{\sqrt{82}}{2}
$