(4x-5)(x-9)/(x-9)=0

Solution for (4x-5)(x-9)/(x-9)=0 equation:

(4x-5)(x-9)/(x-9)=0


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

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

x!=9

x∈R


We multiply parentheses ..

(+4x^2-36x-5x+45)/(x-9)=0

We multiply all the terms by the denominator


(+4x^2-36x-5x+45)=0

We get rid of parentheses

4x^2-36x-5x+45=0

We add all the numbers together, and all the variables

4x^2-41x+45=0

a = 4; b = -41; c = +45;
Δ = b2-4ac
Δ = -412-4·4·45
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-31}{2*4}=\frac{10}{8}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+31}{2*4}=\frac{72}{8}
=9
$