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

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

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

We multiply parentheses ..

(+5x^2-45x-9x+81)=0

We get rid of parentheses

5x^2-45x-9x+81=0

We add all the numbers together, and all the variables

5x^2-54x+81=0

a = 5; b = -54; c = +81;
Δ = b2-4ac
Δ = -542-4·5·81
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-36}{2*5}=\frac{18}{10}
=1+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+36}{2*5}=\frac{90}{10}
=9
$