(4b^2-27b-81)/(b-9)=0

Solution for (4b^2-27b-81)/(b-9)=0 equation:

(4b^2-27b-81)/(b-9)=0


Domain of the equation: (b-9)!=0

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

b!=9

b∈R


We multiply all the terms by the denominator


(4b^2-27b-81)=0

We get rid of parentheses

4b^2-27b-81=0

a = 4; b = -27; c = -81;
Δ = b2-4ac
Δ = -272-4·4·(-81)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-45}{2*4}=\frac{-18}{8}
=-2+1/4
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+45}{2*4}=\frac{72}{8}
=9
$