8(5r-4)(5r-1)=0

Solution for 8(5r-4)(5r-1)=0 equation:

8(5r-4)(5r-1)=0

We multiply parentheses ..

8(+25r^2-5r-20r+4)=0

We multiply parentheses

200r^2-40r-160r+32=0

We add all the numbers together, and all the variables

200r^2-200r+32=0

a = 200; b = -200; c = +32;
Δ = b2-4ac
Δ = -2002-4·200·32
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-120}{2*200}=\frac{80}{400}
=1/5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+120}{2*200}=\frac{320}{400}
=4/5
$