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

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

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

We multiply parentheses ..

(+36x^2-20x-45x+25)=0

We get rid of parentheses

36x^2-20x-45x+25=0

We add all the numbers together, and all the variables

36x^2-65x+25=0

a = 36; b = -65; c = +25;
Δ = b2-4ac
Δ = -652-4·36·25
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-25}{2*36}=\frac{40}{72}
=5/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+25}{2*36}=\frac{90}{72}
=1+1/4
$