(5x-1)(4x-9)=0

Solution for (5x-1)(4x-9)=0 equation:

(5x-1)(4x-9)=0

We multiply parentheses ..

(+20x^2-45x-4x+9)=0

We get rid of parentheses

20x^2-45x-4x+9=0

We add all the numbers together, and all the variables

20x^2-49x+9=0

a = 20; b = -49; c = +9;
Δ = b2-4ac
Δ = -492-4·20·9
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-41}{2*20}=\frac{8}{40}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+41}{2*20}=\frac{90}{40}
=2+1/4
$