-4-5-b=1/3b+16

Solution for -4-5-b=1/3b+16 equation:

-4-5-b=1/3b+16

We move all terms to the left:

-4-5-b-(1/3b+16)=0


Domain of the equation: 3b+16)!=0

b∈R


We add all the numbers together, and all the variables

-1b-(1/3b+16)-9=0

We get rid of parentheses

-1b-1/3b-16-9=0

We multiply all the terms by the denominator


-1b*3b-16*3b-9*3b-1=0

Wy multiply elements

-3b^2-48b-27b-1=0

We add all the numbers together, and all the variables

-3b^2-75b-1=0

a = -3; b = -75; c = -1;
Δ = b2-4ac
Δ = -752-4·(-3)·(-1)
Δ = 5613
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{5613}}{2*-3}=\frac{75-\sqrt{5613}}{-6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{5613}}{2*-3}=\frac{75+\sqrt{5613}}{-6}
$