9p-9p^2=1

Solution for 9p-9p^2=1 equation:

9p-9p^2=1

We move all terms to the left:

9p-9p^2-(1)=0

a = -9; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·(-9)·(-1)
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{5}}{2*-9}=\frac{-9-3\sqrt{5}}{-18}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{5}}{2*-9}=\frac{-9+3\sqrt{5}}{-18}
$