(5p+1)(p-8)=0

Solution for (5p+1)(p-8)=0 equation:

(5p+1)(p-8)=0

We multiply parentheses ..

(+5p^2-40p+p-8)=0

We get rid of parentheses

5p^2-40p+p-8=0

We add all the numbers together, and all the variables

5p^2-39p-8=0

a = 5; b = -39; c = -8;
Δ = b2-4ac
Δ = -392-4·5·(-8)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-41}{2*5}=\frac{-2}{10}
=-1/5
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+41}{2*5}=\frac{80}{10}
=8
$