(3x-9)(5x-20)=0

Solution for (3x-9)(5x-20)=0 equation:

(3x-9)(5x-20)=0

We multiply parentheses ..

(+15x^2-60x-45x+180)=0

We get rid of parentheses

15x^2-60x-45x+180=0

We add all the numbers together, and all the variables

15x^2-105x+180=0

a = 15; b = -105; c = +180;
Δ = b2-4ac
Δ = -1052-4·15·180
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-15}{2*15}=\frac{90}{30}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+15}{2*15}=\frac{120}{30}
=4
$