1/2b+2=3/4b

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

1/2b+2=3/4b

We move all terms to the left:

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


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: 4b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


4b/8b^2+(-6b)/8b^2+2=0

We multiply all the terms by the denominator


4b+(-6b)+2*8b^2=0

Wy multiply elements

16b^2+4b+(-6b)=0

We get rid of parentheses

16b^2+4b-6b=0

We add all the numbers together, and all the variables

16b^2-2b=0

a = 16; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·16·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*16}=\frac{0}{32}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*16}=\frac{4}{32}
=1/8
$