5/3b-11=8/b+4

Solution for 5/3b-11=8/b+4 equation:

5/3b-11=8/b+4

We move all terms to the left:

5/3b-11-(8/b+4)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R



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

b∈R


We get rid of parentheses

5/3b-8/b-4-11=0

We calculate fractions


5b/3b^2+(-24b)/3b^2-4-11=0

We add all the numbers together, and all the variables

5b/3b^2+(-24b)/3b^2-15=0

We multiply all the terms by the denominator


5b+(-24b)-15*3b^2=0

Wy multiply elements

-45b^2+5b+(-24b)=0

We get rid of parentheses

-45b^2+5b-24b=0

We add all the numbers together, and all the variables

-45b^2-19b=0

a = -45; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·(-45)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*-45}=\frac{0}{-90}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*-45}=\frac{38}{-90}
=-19/45
$