1/2b=1/8b+84

Solution for 1/2b=1/8b+84 equation:

1/2b=1/8b+84

We move all terms to the left:

1/2b-(1/8b+84)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: 8b+84)!=0

b∈R


We get rid of parentheses

1/2b-1/8b-84=0

We calculate fractions


8b/16b^2+(-2b)/16b^2-84=0

We multiply all the terms by the denominator


8b+(-2b)-84*16b^2=0

Wy multiply elements

-1344b^2+8b+(-2b)=0

We get rid of parentheses

-1344b^2+8b-2b=0

We add all the numbers together, and all the variables

-1344b^2+6b=0

a = -1344; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-1344)·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*-1344}=\frac{-12}{-2688}
=1/224
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-1344}=\frac{0}{-2688}
=0
$