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

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

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

We move all terms to the left:

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


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R



Domain of the equation: 2b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


2b/8b^2+4b/8b^2-3+1=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

6b-2*8b^2=0

Wy multiply elements

-16b^2+6b=0

a = -16; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-16)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-16}=\frac{-12}{-32}
=3/8
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-16}=\frac{0}{-32}
=0
$