a=41/2a

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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} $

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