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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-(8(+30r^2+48r+25r+40))=0


We calculate terms in parentheses: -(8(+30r^2+48r+25r+40)), so:

8(+30r^2+48r+25r+40)

We multiply parentheses

240r^2+384r+200r+320

We add all the numbers together, and all the variables

240r^2+584r+320

Back to the equation:

-(240r^2+584r+320)


We get rid of parentheses

-240r^2-584r-320=0

a = -240; b = -584; c = -320;
Δ = b2-4ac
Δ = -5842-4·(-240)·(-320)
Δ = 33856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{33856}=184$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-584)-184}{2*-240}=\frac{400}{-480}
=-5/6
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-584)+184}{2*-240}=\frac{768}{-480}
=-1+3/5
$