24/b+3=45/3b

Solution for 24/b+3=45/3b equation:

24/b+3=45/3b

We move all terms to the left:

24/b+3-(45/3b)=0


Domain of the equation: b!=0

b∈R



Domain of the equation: 3b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

24/b-(+45/3b)+3=0

We get rid of parentheses

24/b-45/3b+3=0

We calculate fractions


72b/3b^2+(-45b)/3b^2+3=0

We multiply all the terms by the denominator


72b+(-45b)+3*3b^2=0

Wy multiply elements

9b^2+72b+(-45b)=0

We get rid of parentheses

9b^2+72b-45b=0

We add all the numbers together, and all the variables

9b^2+27b=0

a = 9; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·9·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*9}=\frac{-54}{18}
=-3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*9}=\frac{0}{18}
=0
$