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

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

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

We move all terms to the left:

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


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R



Domain of the equation: 2b+4)!=0

b∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-48b^2+2b+(-4b)=0

We get rid of parentheses

-48b^2+2b-4b=0

We add all the numbers together, and all the variables

-48b^2-2b=0

a = -48; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-48)·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*-48}=\frac{0}{-96}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-48}=\frac{4}{-96}
=-1/24
$