(5x-11)(X-9)=0

Solution for (5x-11)(X-9)=0 equation:

(5x-11)(x-9)=0

We multiply parentheses ..

(+5x^2-45x-11x+99)=0

We get rid of parentheses

5x^2-45x-11x+99=0

We add all the numbers together, and all the variables

5x^2-56x+99=0

a = 5; b = -56; c = +99;
Δ = b2-4ac
Δ = -562-4·5·99
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-34}{2*5}=\frac{22}{10}
=2+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+34}{2*5}=\frac{90}{10}
=9
$