(p-5)(9p+8)=0

Solution for (p-5)(9p+8)=0 equation:

(p-5)(9p+8)=0

We multiply parentheses ..

(+9p^2+8p-45p-40)=0

We get rid of parentheses

9p^2+8p-45p-40=0

We add all the numbers together, and all the variables

9p^2-37p-40=0

a = 9; b = -37; c = -40;
Δ = b2-4ac
Δ = -372-4·9·(-40)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-53}{2*9}=\frac{-16}{18}
=-8/9
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+53}{2*9}=\frac{90}{18}
=5
$