11/b=3/4b+8

Solution for 11/b=3/4b+8 equation:

11/b=3/4b+8

We move all terms to the left:

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


Domain of the equation: b!=0

b∈R



Domain of the equation: 4b+8)!=0

b∈R


We get rid of parentheses

11/b-3/4b-8=0

We calculate fractions


44b/4b^2+(-3b)/4b^2-8=0

We multiply all the terms by the denominator


44b+(-3b)-8*4b^2=0

Wy multiply elements

-32b^2+44b+(-3b)=0

We get rid of parentheses

-32b^2+44b-3b=0

We add all the numbers together, and all the variables

-32b^2+41b=0

a = -32; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·(-32)·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*-32}=\frac{-82}{-64}
=1+9/32
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*-32}=\frac{0}{-64}
=0
$