9(p-4)p=9

Solution for 9(p-4)p=9 equation:

9(p-4)p=9

We move all terms to the left:

9(p-4)p-(9)=0

We multiply parentheses

9p^2-36p-9=0

a = 9; b = -36; c = -9;
Δ = b2-4ac
Δ = -362-4·9·(-9)
Δ = 1620
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-18\sqrt{5}}{2*9}=\frac{36-18\sqrt{5}}{18}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+18\sqrt{5}}{2*9}=\frac{36+18\sqrt{5}}{18}
$