(9x-12)(5x+20)=0

Solution for (9x-12)(5x+20)=0 equation:

(9x-12)(5x+20)=0

We multiply parentheses ..

(+45x^2+180x-60x-240)=0

We get rid of parentheses

45x^2+180x-60x-240=0

We add all the numbers together, and all the variables

45x^2+120x-240=0

a = 45; b = 120; c = -240;
Δ = b2-4ac
Δ = 1202-4·45·(-240)
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-240}{2*45}=\frac{-360}{90}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+240}{2*45}=\frac{120}{90}
=1+1/3
$