72(p^2-1)-17p=0

Solution for 72(p^2-1)-17p=0 equation:

72(p^2-1)-17p=0

We add all the numbers together, and all the variables

-17p+72(p^2-1)=0

We multiply parentheses

72p^2-17p-72=0

a = 72; b = -17; c = -72;
Δ = b2-4ac
Δ = -172-4·72·(-72)
Δ = 21025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21025}=145$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-145}{2*72}=\frac{-128}{144}
=-8/9
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+145}{2*72}=\frac{162}{144}
=1+1/8
$