1/2(2b)=b

Solution for 1/2(2b)=b equation:

1/2(2b)=b

We move all terms to the left:

1/2(2b)-(b)=0


Domain of the equation: 22b!=0

b!=0/22

b!=0

b∈R


We add all the numbers together, and all the variables

-1b+1/22b=0

We multiply all the terms by the denominator


-1b*22b+1=0

Wy multiply elements

-22b^2+1=0

a = -22; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-22)·1
Δ = 88
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{22}}{2*-22}=\frac{0-2\sqrt{22}}{-44}
=-\frac{2\sqrt{22}}{-44}
=-\frac{\sqrt{22}}{-22}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{22}}{2*-22}=\frac{0+2\sqrt{22}}{-44}
=\frac{2\sqrt{22}}{-44}
=\frac{\sqrt{22}}{-22}
$