5/2b-6-1/8=1/8b-24

Solution for 5/2b-6-1/8=1/8b-24 equation:

5/2b-6-1/8=1/8b-24

We move all terms to the left:

5/2b-6-1/8-(1/8b-24)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: 8b-24)!=0

b∈R


We get rid of parentheses

5/2b-1/8b+24-6-1/8=0

We calculate fractions


2560b/1024b^2+(-2b)/1024b^2+(-2b)/1024b^2+24-6=0

We add all the numbers together, and all the variables

2560b/1024b^2+(-2b)/1024b^2+(-2b)/1024b^2+18=0

We multiply all the terms by the denominator


2560b+(-2b)+(-2b)+18*1024b^2=0

Wy multiply elements

18432b^2+2560b+(-2b)+(-2b)=0

We get rid of parentheses

18432b^2+2560b-2b-2b=0

We add all the numbers together, and all the variables

18432b^2+2556b=0

a = 18432; b = 2556; c = 0;
Δ = b2-4ac
Δ = 25562-4·18432·0
Δ = 6533136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6533136}=2556$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2556)-2556}{2*18432}=\frac{-5112}{36864}
=-71/512
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2556)+2556}{2*18432}=\frac{0}{36864}
=0
$