(-11x^2+20x-9)/(x-1)=0

Solution for (-11x^2+20x-9)/(x-1)=0 equation:

(-11x^2+20x-9)/(x-1)=0


Domain of the equation: (x-1)!=0

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

x!=1

x∈R


We multiply all the terms by the denominator


(-11x^2+20x-9)=0

We get rid of parentheses

-11x^2+20x-9=0

a = -11; b = 20; c = -9;
Δ = b2-4ac
Δ = 202-4·(-11)·(-9)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2}{2*-11}=\frac{-22}{-22}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2}{2*-11}=\frac{-18}{-22}
=9/11
$