1/2b-1/4b=1/2-3

Solution for 1/2b-1/4b=1/2-3 equation:

1/2b-1/4b=1/2-3

We move all terms to the left:

1/2b-1/4b-(1/2-3)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R


We get rid of parentheses

1/2b-1/4b+3-1/2=0

We calculate fractions


4b/32b^2+(-8b)/32b^2+(-4b)/32b^2+3=0

We multiply all the terms by the denominator


4b+(-8b)+(-4b)+3*32b^2=0

Wy multiply elements

96b^2+4b+(-8b)+(-4b)=0

We get rid of parentheses

96b^2+4b-8b-4b=0

We add all the numbers together, and all the variables

96b^2-8b=0

a = 96; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·96·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*96}=\frac{0}{192}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*96}=\frac{16}{192}
=1/12
$