2a=1/2a+21

Solution for 2a=1/2a+21 equation:

2a=1/2a+21

We move all terms to the left:

2a-(1/2a+21)=0


Domain of the equation: 2a+21)!=0

a∈R


We get rid of parentheses

2a-1/2a-21=0

We multiply all the terms by the denominator


2a*2a-21*2a-1=0

Wy multiply elements

4a^2-42a-1=0

a = 4; b = -42; c = -1;
Δ = b2-4ac
Δ = -422-4·4·(-1)
Δ = 1780
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:

$\sqrt{\Delta}=\sqrt{1780}=\sqrt{4*445}=\sqrt{4}*\sqrt{445}=2\sqrt{445}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{445}}{2*4}=\frac{42-2\sqrt{445}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{445}}{2*4}=\frac{42+2\sqrt{445}}{8}
$