36(p2-1)=65p

Solution for 36(p2-1)=65p equation:

36(p2-1)=65p

We move all terms to the left:

36(p2-1)-(65p)=0

We add all the numbers together, and all the variables

36(+p^2-1)-65p=0

We multiply parentheses

36p^2-65p-36=0

a = 36; b = -65; c = -36;
Δ = b2-4ac
Δ = -652-4·36·(-36)
Δ = 9409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9409}=97$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-97}{2*36}=\frac{-32}{72}
=-4/9
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+97}{2*36}=\frac{162}{72}
=2+1/4
$