(4r+8)(9r-2)=0

Solution for (4r+8)(9r-2)=0 equation:

(4r+8)(9r-2)=0

We multiply parentheses ..

(+36r^2-8r+72r-16)=0

We get rid of parentheses

36r^2-8r+72r-16=0

We add all the numbers together, and all the variables

36r^2+64r-16=0

a = 36; b = 64; c = -16;
Δ = b2-4ac
Δ = 642-4·36·(-16)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-80}{2*36}=\frac{-144}{72}
=-2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+80}{2*36}=\frac{16}{72}
=2/9
$