(9r+5)(4r-12)=0

Solution for (9r+5)(4r-12)=0 equation:

(9r+5)(4r-12)=0

We multiply parentheses ..

(+36r^2-108r+20r-60)=0

We get rid of parentheses

36r^2-108r+20r-60=0

We add all the numbers together, and all the variables

36r^2-88r-60=0

a = 36; b = -88; c = -60;
Δ = b2-4ac
Δ = -882-4·36·(-60)
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-128}{2*36}=\frac{-40}{72}
=-5/9
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+128}{2*36}=\frac{216}{72}
=3
$