2+1/2b=4b-4

Solution for 2+1/2b=4b-4 equation:

2+1/2b=4b-4

We move all terms to the left:

2+1/2b-(4b-4)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We get rid of parentheses

1/2b-4b+4+2=0

We multiply all the terms by the denominator


-4b*2b+4*2b+2*2b+1=0

Wy multiply elements

-8b^2+8b+4b+1=0

We add all the numbers together, and all the variables

-8b^2+12b+1=0

a = -8; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·(-8)·1
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{11}}{2*-8}=\frac{-12-4\sqrt{11}}{-16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{11}}{2*-8}=\frac{-12+4\sqrt{11}}{-16}
$