(3r-8)(8r+9)=0

Solution for (3r-8)(8r+9)=0 equation:

(3r-8)(8r+9)=0

We multiply parentheses ..

(+24r^2+27r-64r-72)=0

We get rid of parentheses

24r^2+27r-64r-72=0

We add all the numbers together, and all the variables

24r^2-37r-72=0

a = 24; b = -37; c = -72;
Δ = b2-4ac
Δ = -372-4·24·(-72)
Δ = 8281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8281}=91$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-91}{2*24}=\frac{-54}{48}
=-1+1/8
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+91}{2*24}=\frac{128}{48}
=2+2/3
$