3/4b-1/8b=11

Solution for 3/4b-1/8b=11 equation:

3/4b-1/8b=11

We move all terms to the left:

3/4b-1/8b-(11)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R



Domain of the equation: 8b!=0

b!=0/8

b!=0

b∈R


We calculate fractions


24b/32b^2+(-4b)/32b^2-11=0

We multiply all the terms by the denominator


24b+(-4b)-11*32b^2=0

Wy multiply elements

-352b^2+24b+(-4b)=0

We get rid of parentheses

-352b^2+24b-4b=0

We add all the numbers together, and all the variables

-352b^2+20b=0

a = -352; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-352)·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*-352}=\frac{-40}{-704}
=5/88
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-352}=\frac{0}{-704}
=0
$