8(r-5)(r+6)=0

Solution for 8(r-5)(r+6)=0 equation:

8(r-5)(r+6)=0

We multiply parentheses ..

8(+r^2+6r-5r-30)=0

We multiply parentheses

8r^2+48r-40r-240=0

We add all the numbers together, and all the variables

8r^2+8r-240=0

a = 8; b = 8; c = -240;
Δ = b2-4ac
Δ = 82-4·8·(-240)
Δ = 7744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7744}=88$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-88}{2*8}=\frac{-96}{16}
=-6
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+88}{2*8}=\frac{80}{16}
=5
$