5/(2b+19)-9=3b

Solution for 5/(2b+19)-9=3b equation:

5/(2b+19)-9=3b

We move all terms to the left:

5/(2b+19)-9-(3b)=0


Domain of the equation: (2b+19)!=0

We move all terms containing b to the left, all other terms to the right

2b!=-19

b!=-19/2

b!=-9+1/2

b∈R


We add all the numbers together, and all the variables

-3b+5/(2b+19)-9=0

We multiply all the terms by the denominator


-3b*(2b+19)-9*(2b+19)+5=0

We multiply parentheses

-6b^2-57b-18b-171+5=0

We add all the numbers together, and all the variables

-6b^2-75b-166=0

a = -6; b = -75; c = -166;
Δ = b2-4ac
Δ = -752-4·(-6)·(-166)
Δ = 1641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-\sqrt{1641}}{2*-6}=\frac{75-\sqrt{1641}}{-12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{1641}}{2*-6}=\frac{75+\sqrt{1641}}{-12}
$