1/8b-3/4b=5

Solution for 1/8b-3/4b=5 equation:

1/8b-3/4b=5

We move all terms to the left:

1/8b-3/4b-(5)=0


Domain of the equation: 8b!=0

b!=0/8

b!=0

b∈R



Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R


We calculate fractions


4b/32b^2+(-24b)/32b^2-5=0

We multiply all the terms by the denominator


4b+(-24b)-5*32b^2=0

Wy multiply elements

-160b^2+4b+(-24b)=0

We get rid of parentheses

-160b^2+4b-24b=0

We add all the numbers together, and all the variables

-160b^2-20b=0

a = -160; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-160)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*-160}=\frac{0}{-320}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-160}=\frac{40}{-320}
=-1/8
$